Foto Pesquisadores

Mikhail V. Solodov

Institute for Pure and Applied Mathematics
IMPA, Estrada Dona Castorina 110
Jardim Botanico
Rio de Janeiro
RJ, CEP 22460-320, Brazil

Tel: (55-21) 2529-5228
Fax: (55-21) 2529-5129
E-mail: image
               
http://www.cs.wisc.edu/~solodov/solodov.html
http://www.impa.br/~optim/solodov.html

Foto Pesquisadores


Interests: optimization - mathematical programming - operations research


Research Summary

  • Newton and Newton-related algorithms for optimization and variational problems (especially, under weaker-than-standard assumptions).
  • Bundle methods for nonsmooth optimization, decomposition, and inexact proximal-point-related methods.
  • Theory and algorithms for solving variational and complementarity problems.
  • Optimization problems with degenerate constraints, including problems with equilibrium constraints. Relaxed regularity concepts.
  • 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



PUBLICATIONS

Books and Edited Volumes

  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 Methods and Software, Vol. 23, February 2008. [Contents]
    (9 papers, dedicated to the memory of Prof. Naum Shor)
    Boris Mordukhovich, Mikhail Solodov and Michael Todd (Editors).
     
  3.   Optimization, Volume 2: Computational Methods.
    Alexey Izmailov and Mikhail Solodov.
    Rio de Janeiro, Brazil, 2007; Second Edition 2012.
    (In Portuguese, 458 pages. ISBN: 978-85-244-0268-5).
    [ Prefácio ] [Conteúdo] [Compras]
     
  4.   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. ISBN: 978-85-244-0389-7 (In Portuguese, 274 pages).
    [ Prefácio ] [Conteúdo] [Compras]
     
  5.   Optimization Methods and Software, Vol. 19, October 2004. [Contents]
    (11 papers, dedicated to Olvi Mangasarian).
    M.C. Ferris and M.V. Solodov (Editors).
     
  6.   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 ]

Research Articles

  1.   Subdifferential enlargements and continuity properties of the VU-decomposition in convex optimization. [ pdf ]
    Shuai Liu, Claudia Sagastizábal, and Mikhail Solodov
    September 2017.
     
  2.   Local attractors of Newton-type methods for constrained equations and complementarity problems with nonisolated solutions. [ pdf ]
    A. Fischer, A. Izmailov, and M. Solodov
    September 2017.
     
  3.   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
    March 2017.
    Computational Optimization and Applications, 2017.
     
  4.   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, 2017.
     
  5.   Critical solutions of nonlinear equations: Stability issues. [ pdf ] [ doi ]
    A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
    Mathematical Programming, 2016.
     
  6.   A doubly stabilized bundle method for nonsmooth convex optimization. [ pdf ] [ doi ]
    Welington de Oliveira and Mikhail Solodov
    Mathematical Programming 156 (2016), 125-159.
     
  7.   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.
     
  8.   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.
     
  9.   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.
     
  10.   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.
     
  11.   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.
     
  12.   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.
     
  13.   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.
     
  14.   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 ]
     
  15.   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.
     
  16.   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.
     
  17.   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.
     
  18.   Complementarity and game-theoretical models for equilibria in energy markets: deterministic and risk-averse formulations. [ pdf ]
    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.
     
  19.   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.
     
  20.   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.
     
  21.   Stabilized sequential quadratic programming: A survey. [ pdf ] [ doi ]
    D. Fernández and M. Solodov
    Pesquisa Operacional 34 (2014), 463-479 (special issue on Nonlinear Programming).
     
  22.   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.
     
  23.   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.
     
  24.   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).
     
  25.   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.
     
  26.   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.
     
  27.   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.
     
  28.   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.
     
  29.   Stabilized SQP revisited. [ pdf ] [ doi ]
    A.F. Izmailov and M.V. Solodov
    Mathematical Programming 133 (2012), 93-120.
     
  30.   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.
     
  31.   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.
     
  32.   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.
     
  33.   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.
     
  34.   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.
     
  35.   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.
     
  36.   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.
     
  37.   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.
     
  38.   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.
     
  39.   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.
     
  40.   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)
     
  41.   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.
     
  42.   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.
     
  43.   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.
     
  44.   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.
     
  45.   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.
     
  46.   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.
     
  47.   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.
     
  48.   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.
     
  49.   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
     
  50.   An explicit descent method for bilevel convex optimization. [ pdf ]
    Mikhail Solodov
    Journal of Convex Analysis 14 (2007), 227-238.
     
  51.   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.
     
  52.   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.
     
  53.   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.
     
  54.   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.
     
  55.   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.
     
  56.   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.
     
  57.   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.
     
  58.   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.
     
  59.   On the sequential quadratically constrained quadratic programming methods. [ pdf ] [ doi ]
    M.V. Solodov
    Mathematics of Operations Research 29 (2004), 64-79.
     
  60.   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.
     
  61.   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.
     
  62.   Merit functions and error bounds for generalized variational inequalities. [ pdf ] [ doi ]
    M.V. Solodov
    Journal of Mathematical Analysis and Applications 287 (2003), 405-414.
     
  63.   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.
     
  64.   Convergence rate analysis of iterative algorithms for solving variational inequality problems. [ pdf ] [ doi ]
    M.V. Solodov
    Mathematical Programming 96 (2003), 513-528.
     
  65.   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.
     
  66.   A new proximal-based globalization strategy for the Josephy-Newton method for variational inequalities. [ ps ] [ doi ]
    M.V. Solodov and B.F. Svaiter
    Optimization Methods and Software 17 (2002), 965-983.
     
  67.   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.
     
  68.   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.
     
  69.   Parallel variable distribution for constrained optimization. [ pdf ] [ doi ]
    C.A. Sagastizábal and M.V. Solodov
    Computational Optimization and Applications 22 (2002), 111-131.
     
  70.   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.
     
  71.   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.
     
  72.   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.
     
  73.   A class of globally convergent algorithms for pseudomonotone variational inequalities. [ ps ]
    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.
     
  74.   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.
     
  75.   Implicit Lagrangian. [ ps ]
    M.V. Solodov
    Encyclopedia of Optimization, C. Floudas and P. Pardalos (editors),
    Kluwer Academic Publishers, 2001.
     
  76.   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.
     
  77.   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.
     
  78.   A comparison of rates of convergence of two inexact proximal point algorithms. [ ps ]
    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.
     
  79.   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.
     
  80.   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.
     
  81.   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.
     
  82.   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.
     
  83.   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.
     
  84.   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.
     
  85.   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.
     
  86.   Some optimization reformulations of the extended linear complementarity problem. [ pdf ] [ doi ]
    M.V. Solodov
    Computational Optimization and Applications 13 (1999), 187-200.
     
  87.   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.
     
  88.   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.
     
  89.   A hybrid projection-proximal point algorithm. [ ps ]
    M.V. Solodov and B.F. Svaiter
    Journal of Convex Analysis 6 (1999), 59-70.
     
  90.   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.
     
  91.   A globally convergent inexact Newton method for systems of monotone equations. [ ps ]
    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.
     
  92.   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.
     
  93.   On the convergence of constrained parallel variable distribution algorithms. [ pdf ] [ doi ]
    M.V. Solodov
    SIAM Journal on Optimization 8 (1998), 187-196.
     
  94.   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.
     
  95.   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.
     
  96.   Incremental gradient algorithms with stepsizes bounded away from zero. [ pdf ] [ doi ]
    M.V. Solodov
    Computational Optimization and Applications 11 (1998), 23-35.
     
  97.   Convergence analysis of perturbed feasible descent methods. [ pdf ] [ doi ]
    M.V. Solodov
    Journal of Optimization Theory and Applications 93 (1997), 337-353.
     
  98.   Minimization of nonsmooth convex functionals in Banach spaces. [ ps ]
    Ya.I. Alber, A.N. Iusem, and M.V. Solodov
    Journal of Convex Analysis 4 (1997), 235-255.
     
  99.   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.
     
  100.   Newton-type methods with generalized distances for constrained optimization. [ ps ] [ doi ]
    A.N. Iusem and M.V. Solodov
    Optimization 41 (1997), 257-278.
     
  101.   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.
     
  102.   New inexact parallel variable distribution algorithms. [ pdf ] [ doi ]
    M.V. Solodov
    Computational Optimization and Applications 7 (1997), 165-182.
     
  103.   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.
     
  104.   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.
     
  105.   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.
     
  106.   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.
     
  107.   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.
     
  108.   Nonlinear complementarity as unconstrained and constrained minimization. [ pdf ] [ doi ]
    O.L. Mangasarian and M.V. Solodov
    Mathematical Programming  62 (1993), 277-297.

Last Updated: September 2017.

Education

PhD in Computer Sciences
        University of Wisconsin - Madison, 1995.
        Advisor Olvi L. Mangasarian ,
        John von Neumann Professor of Mathematics and Computer Sciences

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

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