Mikhail V. Solodov

Interests: optimization - mathematical programming - operations research

Research Summary

• Newton and Newton-related algorithms for optimization and variational problems
  (especially, under weaker-than-standard assumptions).
• Augmented Lagrangian and related techniques.
• Decomposition.
• Nonsmooth optimization, especially (but not only) bundle methods.
• Inexact proximal-point-related methods.
• Generalized Nash Equilibrium Problems, and other equilibrium problems. Including applications to Energy Models.
• Optimization problems with degenerate constraints, including problems with complementarity constraints. Relaxed regularity concepts.
• Theory and algorithms for solving variational and complementarity problems.
• Perturbation and error-stability analysis of computational algorithms.
• Parallel optimization algorithms (former interest).
• Applications of optimization to machine learning (former interest).

Member of Editorial Boards

• SIAM Journal on Optimization (since 2009)
• Mathematical Programming, Series A (since 2005)
• Optimization Methods and Software (since 2002)

Books

1.   Newton-Type Methods for Optimization and Variational Problems.
   Alexey F. Izmailov and Mikhail V. Solodov.
   Springer Series in Operations Research and Financial Engineering, Springer International Publishing, Switzerland, 2014 (573 pages).
   [Springer link with Preface, Table of Contents]
   [List of corrections]
    
2.   Optimization, Volume 2: Computational Methods.
   Alexey Izmailov and Mikhail Solodov.
   Rio de Janeiro, Brazil, 2007; Second Edition 2012, Third Edition 2018.
   (In Portuguese, 494 pages. ISBN: 978-85-244-0454-2).
   [ Prefácio e Conteúdo] [Compras]
    
3.   Optimization, Volume 1: Optimality Conditions, Elements of Convex Analysis and Duality.
   Alexey Izmailov and Mikhail Solodov.
   Rio de Janeiro, Brazil, 2005. ISBN: 85-244-0238-5.
   Second Edition 2009, Third Edition 2014, Fourth Edition 2020. ISBN: 978-65-990528-0-4 (In Portuguese, 274 pages).
   [ Prefácio e Conteúdo] [Compras]
    
4.   Numerical Methods of Optimization.
   A.F. Izmailov and M.V. Solodov.
   Fizmatlit/Nauka, Moscow, Russia, 2003, ISBN: 5-9221-0045-9.
   Second Edition 2008. ISBN: 978-5-9221-0975-8 (In Russian, 320 pages).
   [ Preface and Contents ]

Edited Volumes

1.   Mathematical Programming, Series B, Vol. 198-2, April 2023. [Contents]
   (special issue on Hierarchical Optimization).
   Kristin P. Bennett, Michael C. Ferris, Jong-Shi Pang, Mikhail V. Solodov, and Stephen J. Wright (Editors).
    
2.   Optimization Methods and Software, Vol. 23, February 2008. [Contents]
   (dedicated to the memory of Prof. Naum Shor)
   Boris Mordukhovich, Mikhail Solodov and Michael Todd (Editors).
    
3.   Optimization Methods and Software, Vol. 19, October 2004. [Contents]
   (dedicated to Olvi Mangasarian).
   M.C. Ferris and M.V. Solodov (Editors).

Research Articles

1.   Proximal gradient VU method with superlinear convergence for nonsmooth convex optimization. [ pdf ]
   Shuai Liu, Claudia Sagastizábal, and Mikhail Solodov
   September 2024.
    
2.   Convergence properties of proximal (sub)gradient methods without convexity or smoothness of any of the functions. [ pdf ]
   Mikhail Solodov
   August 2023.
   SIAM Journal on Optimization, to appear.
    
3.   A general perturbed Newtonian framework and critical solutions of nonlinear equations. [ pdf ]
   A. Izmailov and M. Solodov
   July 2024.
    
4.   The Levenberg--Marquardt method: An overview of modern convergence theories and more. [ doi ] [ pdf ]
   A. Fischer, A. Izmailov, and M. Solodov
   Computational Optimization and Applications 89 (2024), 33-67.
    
5.   On local behavior of Newton-type methods near critical solutions of constrained equations. [ doi ] [ pdf ]
   A. Izmailov and M. Solodov
   Journal of Optimization Theory and Applications 203 (2024), 1103-1126.
    
6.   A unified analysis of descent sequences in weakly convex optimization, including convergence rates for bundle methods. [ doi ] [ pdf ]
   Felipe Atenas, Claudia Sagastizábal, Paulo J.S. Silva, and Mikhail Solodov
   SIAM Journal on Optimization 33 (2023), 89-115.
    
7.   Convergence rate estimates for penalty methods revisited. [ doi ] [ pdf ]
   A. Izmailov and M. Solodov
   Computational Optimization and Applications 85 (2023), 973-992.
    
8.   Regularized equilibrium problems with equilibrium constraints with application to energy markets. [ pdf ] [ doi ]
   Juan Pablo Luna, Claudia Sagastizábal, Julia Filiberti, Steve A. Gabriel, and Mikhail Solodov
   SIAM Journal on Optimization 33 (2023), 1767-1796.
    
9.   Profit sharing mechanisms in multi-owned cascaded hydrosystems. [ pdf ] [ doi ]
   Pedro Borges, Claudia Sagastizábal, Mikhail Solodov, Leo Liberti, and Claudia D'Ambrosio
   Optimization and Engineering 24 (2023), 2005-2043.
    
10.   Increasing reliability of price signals in long term energy management problems. [ pdf ] [ doi ]
    Guillaume Erbs, Clara Lage, Claudia Sagastizábal, and Mikhail Solodov
    Computational Optimization and Applications 85 (2023), 787-820.
     
11.   A distributionally-ambiguous two-stage stochastic approach for investment in renewable generation. [ pdf ] [ doi ]
    Pedro Borges, Claudia Sagastizábal, Mikhail Solodov, and Asgeir Tomasgard
    European Journal of Applied Mathematics 34 (2023), 484-504.
     
12.   Perturbed augmented Lagrangian method framework with applications to proximal and smoothed variants. [ pdf ] [ doi ]
    A. Izmailov and M. Solodov
    Journal of Optimization Theory and Applications 193 (2022), 491-522.
     
13.   A regularized smoothing method for fully parameterized convex problems with applications to convex and nonconvex two-stage stochastic programming. [ pdf ] [ doi ]
    Pedro Borges, Claudia Sagastizábal, and Mikhail Solodov
    Mathematical Programming 189 (2021), 117-149.
     
14.   Decomposition algorithms for some deterministic and two-stage stochastic single-leader multi-follower games. [ pdf ] [ doi ]
    Pedro Borges, Claudia Sagastizábal, and Mikhail Solodov
    Computational Optimization and Applications 78 (2021), 675-704.
     
15.   Unit stepsize for the Newton method close to critical solutions. [ pdf ] [ doi ]
    A. Fischer, A. Izmailov, and M. Solodov
    Mathematical Programming 187 (2021), 697-721.
     
16.   Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations. [ pdf ] [ doi ]
    A. Fischer, A. Izmailov, and M. Solodov
    Computational Optimization and Applications 78 (2021), 273-286.
     
17.   A class of Benders decomposition methods for variational inequalities. [ pdf ] [ doi ]
    Juan Pablo Luna, Claudia Sagastizábal, and Mikhail Solodov
    Computational Optimization and Applications 76 (2020), 935-959.
     
18.   Bundle methods for inexact data. [ pdf ] [ doi ]
    Welington de Oliveira and Mikhail Solodov
    In Numerical Nonsmooth Optimization -- State of the Art Algorithms, pages 417-459. A. Bagirov, M. Gaudioso, N. Karmitsa, M. Mäakelä and S. Taheri (editors). Springer, 2020.
     
19.   On the cost of solving augmented Lagrangian subproblems. [ pdf ] [ doi ]
    D. Fernández and M. Solodov
    Mathematical Programming 182 (2020), 37-55.
     
20.   Multiplier stabilization applied to two-stage stochastic programs. [ pdf ] [ doi ]
    Clara Lage, Claudia Sagastizábal, and Mikhail Solodov
    Journal of Optimization Theory and Applications 183 (2019), 158-178.
     
21.   A globally convergent Levenberg--Marquardt method for equality-constrained optimization. [ pdf ] [ doi ]
    A.F. Izmailov, M.V. Solodov, and E.I. Uskov
    Computational Optimization and Applications 72 (2019), 215-239.
     
22.   Subdifferential enlargements and continuity properties of the VU-decomposition in convex optimization. [ pdf ] [ doi ]
    Shuai Liu, Claudia Sagastizábal, and Mikhail Solodov
    In Nonsmooth Optimization and Its Applications, S. Hosseini, B. Mordukhovich, A. Uschmajew (editors). International Series of Numerical Mathematics, vol. 170, pp. 55-87, 2019. Birkhauser, Cham.
     
23.   Local attractors of Newton-type methods for constrained equations and complementarity problems with nonisolated solutions. [ pdf ] [ doi ]
    A. Fischer, A. Izmailov, and M. Solodov
    Journal of Optimization Theory and Applications 180 (2019), 140-169.
     
24.   Critical solutions of nonlinear equations: Local attraction for Newton-type methods. [ pdf ] [ doi ]
    A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
    Mathematical Programming 167 (2018), 355-379.
     
25.   Critical solutions of nonlinear equations: Stability issues. [ pdf ] [ doi ]
    A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
    Mathematical Programming 168 (2018), 475-507.
     
26.   A globally convergent LP--Newton method for piecewise smooth constrained equations: Escaping nonstationary accumulation points. [ pdf ] [ doi ]
    A. Fischer, M. Herrich, A. Izmailov, W. Scheck, and M. Solodov
    Computational Optimization and Applications 69 (2018), 325-349.
     
27.   A doubly stabilized bundle method for nonsmooth convex optimization. [ pdf ] [ doi ]
    Welington de Oliveira and Mikhail Solodov
    Mathematical Programming 156 (2016), 125-159.
     
28.   A globally convergent LP--Newton method. [ pdf ] [ doi ]
    A. Fischer, M. Herrich, A. Izmailov, and M. Solodov
    SIAM Journal on Optimization 26 (2016), 2012-2033.
     
29.   An approximation scheme for a class of risk-averse stochastic equilibrium problems. [ pdf ] [ doi ]
    Juan Pablo Luna, Claudia Sagastizábal, and Mikhail Solodov
    Mathematical Programming 157 (2016), 451-481.
     
30.   Some new facts about sequential quadratic programming methods employing second derivatives. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Optimization Methods and Software 31 (2016), 1111-1131.
     
31.   Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions. [ pdf ] [ doi ]
    A. Fischer, M. Herrich, A. Izmailov, and M. Solodov
    Computational Optimization and Applications 63 (2016), 425-459.
     
32.   Globalizing stabilized sequential quadratic programming method by smooth primal-dual exact penalty function. [ pdf ] [ doi ]
    A.F. Izmailov, M.V. Solodov, and E.I. Uskov
    Journal of Optimization Theory and Applications 169 (2016), 148-178.
     
33.   A proximal bundle method for nonsmooth nonconvex functions with inexact information. [ pdf ] [ doi ]
    Warren Hare, Claudia Sagastizábal, and Mikhail Solodov
    Computational Optimization and Applications 63 (2016), 1-28.
     
34.   Newton-type methods: A broader view. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Journal of Optimization Theory and Applications 164 (2015), 577-620.
     
35.   Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Invited discussion paper, TOP 23 (2015), 1-26.
    This invited paper is discussed in the comments available at [ A. Fischer ], [ J.M. Martínez ], [ B.S. Mordukhovich ], [ D.P. Robinson ].
    Rejoinder on the discussion: TOP 23 (2015), 48-52. [ pdf ] [ doi ]
     
36.   Combining stabilized SQP with the augmented Lagrangian algorithm. [ pdf ] [ doi ]
    A.F. Izmailov, M.V. Solodov, and E.I. Uskov
    Computational Optimization and Applications 62 (2015), 405-429.
     
37.   Some composite-step constrained optimization methods interpreted via the perturbed sequential quadratic programming framework. [ pdf ] [ doi ]
    A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
    Optimization Methods and Software 30 (2015), 461-477.
     
38.   Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption. [ pdf ] [ doi ]
    A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
    Computational Optimization and Applications 60 (2015), 111-140.
     
39.   Complementarity and game-theoretical models for equilibria in energy markets: deterministic and risk-averse formulations. [ pdf ] [ doi ]
    Juan Pablo Luna, Claudia Sagastizábal, and Mikhail Solodov
    In  Handbook of Risk Management for Energy Production and Trading,
    R.M. Kovacevic, G.Ch. Pflug, and M.T. Vespucci (editors), Springer, International Series in Operations Research and Management Science, Vol. 199, Chapter 10, pp. 237-264, 2014.
     
40.   On error bounds and Newton-type methods for generalized Nash equilibrium problems. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Computational Optimization and Applications 59 (2014), 201-218.
     
41.   A class of Dantzig--Wolfe type decomposition methods for variational inequality problems. [ pdf ] [ doi ]
    Juan Pablo Luna, Claudia Sagastizábal, and Mikhail Solodov
    Mathematical Programming 143 (2014), 177-209.
     
42.   Stabilized sequential quadratic programming: A survey. [ pdf ] [ doi ]
    D. Fernández and M. Solodov
    Pesquisa Operacional 34 (2014), 463-479 (special issue on Nonlinear Programming).
     
43.   A note on upper Lipschitz stability, error bounds, and critical multipliers for Lipschitz-continuous KKT systems. [ pdf ] [ doi ]
    A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
    Mathematical Programming 142 (2013), 591-604.
     
44.   The Josephy--Newton method for semismooth generalized equations and semismooth SQP for optimization. [ pdf ] [ doi ]
    A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
    Set-Valued and Variational Analysis 21 (2013), 17-45.
     
45.   Solving net constrained hydrothermal Nash-Cournot equilibrium problems via the proximal decomposition method. [ pdf ]
    L.A. Parente, P.A. Lotito, A.J. Rubiales, and M.V. Solodov
    Pacific Journal of Optimization 9 (2013), 301-322. (special issue on Equilibrium Optimization).
     
46.   Global convergence of augmented Lagrangian methods applied to optimization problems with degenerate constraints, including problems with complementarity constraints. [ pdf ] [ doi ]
    A.F. Izmailov, M.V. Solodov, and E.I. Uskov
    SIAM Journal on Optimization 22 (2012), 1579-1606.
     
47.   Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition. [ pdf ] [ doi ]
    D. Fernández and M. Solodov
    SIAM Journal on Optimization 22 (2012), 384-407.
     
48.   Solving generation expansion planning problems with environmental constraints by a bundle method. [ pdf ] [ doi ]
    Claudia Sagastizábal and Mikhail Solodov
    Computational Management Science 9 (2012), 163-182.
     
49.   Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints. [ pdf ] [ doi ]
    A.F. Izmailov, A.L. Pogosyan, and M.V. Solodov
    Computational Optimization and Applications 51 (2012), 199-221.
     
50.   Stabilized SQP revisited. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematical Programming 133 (2012), 93-120.
     
51.   Semismooth SQP method for equality-constrained optimization problems with an application to the lifted reformulation of mathematical programs with complementarity constraints. [ pdf ] [ doi ]
    A.F. Izmailov, A.L. Pogosyan, and M.V. Solodov
    Optimization Methods and Software 26 (2011), 847-872.
     
52.   The hybrid proximal decomposition method applied to the computation of a Nash equilibrium for hydrothermal electricity markets. [ pdf ] [ doi ]
    L.A. Parente, P.A. Lotito, F.J. Mayorano, A.J. Rubiales, and M.V. Solodov
    Optimization and Engineering 12 (2011), 277-302.
     
53.   On attraction of linearly constrained Lagrangian methods and of stabilized and quasi-Newton SQP methods to critical multipliers. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematical Programming 126 (2011), 231-257.
     
54.   Constraint qualifications. [ pdf ] [ doi ]
    M.V. Solodov
    Wiley Encyclopedia of Operations Research and Management Science [ doi ], James J. Cochran, et al. (editors), John Wiley & Sons, Inc., 2010.
     
55.   Sharp primal superlinear convergence results for some Newtonian methods for constrained optimization. [ pdf ] [ doi ]
    D. Fernández, A.F. Izmailov, and M.V. Solodov
    SIAM Journal on Optimization 20 (2010), 3312-3334.
     
56.   Inexact Josephy--Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Computational Optimization and Applications 46 (2010), 347-368.
     
57.   A truncated SQP method based on inexact interior-point solutions of subproblems. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    SIAM Journal on Optimization 20 (2010), 2584-2613.
     
58.   Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems. [ pdf ] [ doi ]
    Damián Fernández and Mikhail Solodov
    Mathematical Programming 125 (2010), 47-73.
     
59.   Identifying structure of nonsmooth convex functions by the bundle technique. [ pdf ] [ doi ]
    A. Daniilidis, C. Sagastizábal, and M. Solodov
    SIAM Journal on Optimization 20 (2009), 820-840.
     
60.   A class of variable metric decomposition methods for monotone variational inclusions. [ pdf ]
    P.A. Lotito, L.A. Parente, and M.V. Solodov
    Journal of Convex Analysis 16 (2009), 857-880.
     
61.   Examples of dual behaviour of Newton-type methods on optimization problems with degenerate constraints. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Computational Optimization and Applications 42 (2009), 231-264.
    [ DEGEN_collection.zip ] A collection of test problems with degenerate constraints described in this paper (updated and extended version; see Readme.txt for more information)
     
62.   A survey on dual behavior of Newton-type methods for constrained optimization.
    A.F. Izmailov and M.V. Solodov
    In proceedings of the International Conference Nonlinear Analysis and Optimization Problems, Scientific Meetings, Vol. 100, the Section of Natural Sciences, Vol. 13, Podgorica: Montenegrin Academy of Sciences and Arts, 2009, pp. 157-174.
     
63.   Global convergence of an SQP method without boundedness assumptions on any of the iterative sequences. [ pdf ] [ doi ]
    Mikhail Solodov
    Mathematical Programming 118 (2009), 1-12.
     
64.   Mathematical programs with vanishing constraints: optimality conditions, sensitivity, and a relaxation method. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Journal of Optimization Theory and Applications 142 (2009), 501-532.
     
65.   On attraction of Newton-type iterates to multipliers violating second-order sufficiency conditions. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematical Programming 117 (2009), 271-304.
     
66.   A bundle-filter method for nonsmooth convex constrained optimization. [ pdf ] [ doi ]
    E. Karas, A. Ribeiro, C. Sagastizábal, and M. Solodov
    Mathematical Programming 116 (2009), 297-320.
     
67.   A class of inexact variable metric proximal point algorithms. [ pdf ] [ doi ]
    L.A. Parente, P.A. Lotito, and M.V. Solodov
    SIAM Journal on Optimization 19 (2008), 240-260.
     
68.   On local convergence of sequential quadratically-constrained quadratic-programming type methods, with an extension to variational problems. [ pdf ] [ doi ]
    Damián Fernández and Mikhail Solodov
    Computational Optimization and Applications 39 (2008), 143-160.
     
69.   An active set Newton method for mathematical programs with complementarity constraints. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    SIAM Journal on Optimization 19 (2008), 1003-1027.
     
70.   A bundle method for a class of bilevel nonsmooth convex minimization problems. [ pdf ] [ doi ]
    Mikhail Solodov
    SIAM Journal on Optimization 18 (2007), 242-259.
    [ genbi.m ] Matlab generator of problems described in this paper
     
71.   An explicit descent method for bilevel convex optimization. [ pdf ]
    Mikhail Solodov
    Journal of Convex Analysis 14 (2007), 227-238.
     
72.   Primal error bounds based on the augmented Lagrangian and Lagrangian relaxation algorithms. [ pdf ]
    A.F. Izmailov and M.V. Solodov
    Pacific Journal of Optimization 2 (2006), 575-589.
     
73.   A note on error estimates for some interior penalty methods. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    In   Recent Advances in Optimization,
    A. Seeger (editor), Lectures Notes in Economics and Mathematical Systems, Vol. 563, Springer-Verlag Berlin Heidelberg, 2006, pp. 133-145.
     
74.   An infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter. [ pdf ] [ doi ]
    Claudia Sagastizábal and Mikhail Solodov
    SIAM Journal on Optimization 16 (2005), 146-169.
     
75.   Numerical results for a globalized active-set Newton method for mixed complementarity problems. [ pdf ] [ doi ]
    A.N. Daryina, A.F. Izmailov, and M.V. Solodov
    Computational and Applied Mathematics 24 (2005), 293-316.
     
76.   A note on solution sensitivity for Karush-Kuhn-Tucker systems. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematical Methods of Operations Research 61 (2005), 347-363.
     
77.   A class of active-set Newton methods for mixed complementarity problems. [ pdf ] [ doi ]
    A.N. Daryina, A.F. Izmailov, and M.V. Solodov
    SIAM Journal on Optimization 15 (2004/2005), 409-429.
     
78.   A class of decomposition methods for convex optimization and monotone variational inclusions via the hybrid inexact proximal point framework. [ pdf ] [ doi ]
    M.V. Solodov
    Optimization Methods and Software 19 (2004), 557-575.
     
79.   Newton-type methods for optimization problems without constraint qualifications. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    SIAM Journal on Optimization 15 (2004), 210-228.
     
80.   On the sequential quadratically constrained quadratic programming methods. [ pdf ] [ doi ]
    M.V. Solodov
    Mathematics of Operations Research 29 (2004), 64-79.
     
81.   On approximations with finite precision in bundle methods for nonsmooth optimization. [ pdf ] [ doi ]
    M.V. Solodov
    Journal of Optimization Theory and Applications 119 (2003), 151-165.
     
82.   Karush-Kuhn-Tucker systems: regularity conditions, error bounds and a class of Newton-type methods. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematical Programming 95 (2003), 631-650.
     
83.   Merit functions and error bounds for generalized variational inequalities. [ pdf ] [ doi ]
    M.V. Solodov
    Journal of Mathematical Analysis and Applications 287 (2003), 405-414.
     
84.   Globally convergent algorithms of Newton type for optimization problems without regularity of constraints. (in Russian)
    A.F. Izmailov, M.V. Solodov, and K.M. Chokparov
    In  Problems of Modeling and Analysis in Decision Making Problems,
    V.A. Bereznev (editor), Computing Center of the Russian Academy of Sciences, 2003, pp. 63-82.
     
85.   Convergence rate analysis of iterative algorithms for solving variational inequality problems. [ pdf ] [ doi ]
    M.V. Solodov
    Mathematical Programming 96 (2003), 513-528.
     
86.   Superlinearly convergent algorithms for solving singular equations and smooth reformulations of complementarity problems. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    SIAM Journal on Optimization 13 (2002), 386-405.
     
87.   A new proximal-based globalization strategy for the Josephy-Newton method for variational inequalities. [ pdf ] [ doi ]
    M.V. Solodov and B.F. Svaiter
    Optimization Methods and Software 17 (2002), 965-983.
     
88.   The theory of 2-regularity for mappings with Lipschitzian derivatives and its applications to optimality conditions. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematics of Operations Research 27 (2002), 614-635.
     
89.   On optimality conditions for cone-constrained optimization.
    A.F. Izmailov and M.V. Solodov
    In  Proceedings of the 41-st IEEE Conference on Decision and Control, Omnipress, 2002.
     
90.   Parallel variable distribution for constrained optimization. [ pdf ] [ doi ]
    C.A. Sagastizábal and M.V. Solodov
    Computational Optimization and Applications 22 (2002), 111-131.
     
91.   Complementarity constraint qualification via the theory of 2-regularity. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    SIAM Journal on Optimization 13 (2002), 368-385.
     
92.   A unified framework for some inexact proximal point algorithms. [ ps ] [ doi ]
    M.V. Solodov and B.F. Svaiter
    Numerical Functional Analysis and Optimization 22 (2001), 1013-1035.
     
93.   Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematical Programming 89 (2001), 413-435.
     
94.   A class of globally convergent algorithms for pseudomonotone variational inequalities. [ ps ] [ doi ]
    M.V. Solodov
    In  Complementarity: Applications, Algorithms and Extensions,
    M C. Ferris, O.L. Mangasarian and J.-S. Pang (editors), Applied Optimization 50, Kluwer Academic Publishers, 2001, Chapter 14, pp. 297-315.
     
95.   Optimality conditions for irregular inequality-constrained problems. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    SIAM Journal on Control and Optimization 40 (2001/2002), 1280-1295.
     
96.   Implicit Lagrangian. [ ps ] [ doi ]
    M.V. Solodov
    Encyclopedia of Optimization, C. Floudas and P. Pardalos (editors),
    Kluwer Academic Publishers, 2001.
     
97.   On the relation between bundle methods for maximal monotone inclusions and hybrid proximal point algorithms.
    C.A. Sagastizábal and M.V. Solodov
    In   Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications,
    D. Butnariu, Y. Censor and S. Reich (editors), Studies in Computational Mathematics 8, Elsevier Science B.V., 2001, pp. 441-455.
     
98.   Error bounds for proximal point subproblems and associated inexact proximal point algorithms. [ pdf ] [ doi ]
    M.V. Solodov and B.F. Svaiter
    Mathematical Programming 88 (2000), 371-389.
     
99.   A comparison of rates of convergence of two inexact proximal point algorithms. [ ps ] [ doi ]
    M.V. Solodov and B.F. Svaiter
    In  Nonlinear Optimization and Related Topics,
    G. Di Pillo and F. Giannessi (editors), Applied Optimization 36, Kluwer Academic Publishers, 2000, pp. 415-427.
     
100.   Some methods based on the D-gap function for solving monotone variational inequalities. [ pdf ] [ doi ]
     M.V. Solodov and P. Tseng
     Computational Optimization and Applications 17 (2000), 255-277.
      
101.   An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions. [ pdf ] [ doi ]
     M.V. Solodov and B.F. Svaiter
     Mathematics of Operations Research 25 (2000), 214-230.
      
102.   A truly globally convergent Newton-type method for the monotone nonlinear complementarity problem. [ pdf ] [ doi ]
     M.V. Solodov and B.F. Svaiter
     SIAM Journal on Optimization 10 (2000), 605-625.
      
103.   The theory of 2-regularity for mappings with Lipschitz derivatives and its applications. (in Russian; a summary of related publications in English) [ ps ]
     A.F. Izmailov and M.V. Solodov
     In  Problems of Modeling and Analysis in Decision Making Problems,
     V.A. Bereznev, V.G. Karmanov and A.A. Tretyakov (editors), Computing Center of the Russian Academy of Sciences, 2000, pp. 26-50.
      
104.   Forcing strong convergence of proximal point iterations in a Hilbert space. [ pdf ] [ doi ]
     M.V. Solodov and B.F. Svaiter
     Mathematical Programming 87 (2000), 189-202.
      
105.   A linearly convergent derivative-free descent method for strongly monotone complementarity problems. [ pdf ] [ doi ]
     O.L. Mangasarian and M.V. Solodov
     Computational Optimization and Applications 14 (1999), 5-16.
      
106.   A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator. [ pdf ] [ doi ]
     M.V. Solodov and B.F. Svaiter
     Set-Valued Analysis 7 (1999), 323-345.
      
107.   Some optimization reformulations of the extended linear complementarity problem. [ pdf ] [ doi ]
     M.V. Solodov
     Computational Optimization and Applications 13 (1999), 187-200.
      
108.   A new projection method for variational inequality problems. [ pdf ] [ doi ]
     M.V. Solodov and B.F. Svaiter
     SIAM Journal on Control and Optimization 37 (1999), 765-776.
      
109.   Parallel constrained optimization via distribution of variables.
     C.A. Sagastizábal and M.V. Solodov
     In  Lecture Notes in Computer Science, Vol. 1685, pp. 1112-1119, P. Amestoy et al. (editors),
     Springer-Verlag, 1999.
      
110.   A hybrid projection-proximal point algorithm. [ pdf ]
     M.V. Solodov and B.F. Svaiter
     Journal of Convex Analysis 6 (1999), 59-70.
      
111.   Globalization strategies in successive linearization methods for variational inequalities.
     M.V. Solodov
     In  Actas de VI Congreso de Matematica Aplicada, R. Montenegro,G. Montero and G. Winter (editors), Universidad de Las Palmas de Gran Canaria, 1999, pp. 1307-1314.
      
112.   A globally convergent inexact Newton method for systems of monotone equations. [ ps ] [ doi ]
     M.V. Solodov and B.F. Svaiter
     In  Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods ,
     M. Fukushima and L. Qi (editors), Applied Optimization 22, Kluwer Academic Publishers, 1999,
     pp. 355-369.
      
113.   A projection-type method for pseudomonotone variational inequality problems.
     M.V. Solodov and B.F. Svaiter
     In  Proceedings of the 38-th IEEE Conference on Decision and Control, Omnipress, 1999, pp. 2569-2574.
      
114.   On the convergence of constrained parallel variable distribution algorithms. [ pdf ] [ doi ]
     M.V. Solodov
     SIAM Journal on Optimization 8 (1998), 187-196.
      
115.   Error stability properties of generalized gradient-type algorithms. [ pdf ] [ doi ]
     M.V. Solodov and S.K. Zavriev
     Journal of Optimization Theory and Applications 98 (1998), 663-680.
      
116.   On the projected subgradient method for nonsmooth convex optimization in a Hilbert space. [ pdf ] [ doi ]
     Ya.I. Alber, A.N. Iusem, and M.V. Solodov
     Mathematical Programming 81 (1998), 23-35.
      
117.   Incremental gradient algorithms with stepsizes bounded away from zero. [ pdf ] [ doi ]
     M.V. Solodov
     Computational Optimization and Applications 11 (1998), 23-35.
      
118.   Convergence analysis of perturbed feasible descent methods. [ pdf ] [ doi ]
     M.V. Solodov
     Journal of Optimization Theory and Applications 93 (1997), 337-353.
      
119.   Minimization of nonsmooth convex functionals in Banach spaces. [ pdf ]
     Ya.I. Alber, A.N. Iusem, and M.V. Solodov
     Journal of Convex Analysis 4 (1997), 235-255.
      
120.   Descent methods with linesearch in the presence of perturbations. [ doi ]
     M.V. Solodov and B.F. Svaiter
     Journal of Computational and Applied Mathematics 80 (1997), 265-275.
      
121.   Newton-type methods with generalized distances for constrained optimization. [ ps ] [ doi ]
     A.N. Iusem and M.V. Solodov
     Optimization 41 (1997), 257-278.
      
122.   Stationary points of bound constrained minimization reformulations of complementarity problems. [ pdf ] [ doi ]
     M.V. Solodov
     Journal of Optimization Theory and Applications 94 (1997), 449-467.
      
123.   New inexact parallel variable distribution algorithms. [ pdf ] [ doi ]
     M.V. Solodov
     Computational Optimization and Applications 7 (1997), 165-182.
      
124.   Modified projection-type methods for monotone variational inequalities. [ ps ] [ doi ]
     M.V. Solodov and P. Tseng
     SIAM Journal on Control and Optimization 34 (1996), 1814-1830.
      
125.   Nonmonotone and Perturbed Optimization, Ph.D. Dissertation.
     M.V. Solodov
     Mathematical Programming Technical Report 95-13,
     Computer Sciences Department, University of Wisconsin,
     1210 West Dayton Street, Madison, Wisconsin 53706, U.S.A., August 1995.
      
126.   Serial and parallel backpropagation convergence via nonmonotone perturbed minimization. [ ps ] [ doi ]
     O.L. Mangasarian and M.V. Solodov
     Optimization Methods and Software 4 (1994), 103-116.
      
127.   New error bounds for the linear complementarity problems. [ ps ] [ doi ]
     Z.-Q. Luo, O.L. Mangasarian, J. Ren, and M.V. Solodov
     Mathematics of Operations Research 19 (1994), 880-892.
      
128.   Backpropagation convergence via deterministic perturbed minimization. [ ps ]
     O.L. Mangasarian and M.V. Solodov
     In  Advances in Neural Information Processing Systems , Vol. 6, pp. 383-390,
     J.D. Cowan, G. Tesauro and J. Alspector (editors), Morgan Kaufmann Publishers, 1994.
      
129.   Nonlinear complementarity as unconstrained and constrained minimization. [ pdf ] [ doi ]
     O.L. Mangasarian and M.V. Solodov
     Mathematical Programming  62 (1993), 277-297.

Education

MS in Computer Sciences
       University of Wisconsin - Madison, 1992.

Diploma (with Honors)
       Department of Computational Mathematics and Cybernetics,
       Moscow State University, 1991.