Mikhail V. Solodov

Interests: optimization - mathematical programming - operations research

Research Summary

• Theory and algorithms for solving variational and complementarity problems.
• Bundle, decomposition and inexact proximal-point-related methods.
• Regularity concepts and Newton-type algorithms under weak regularity conditions.
• Perturbation and error-stability analysis of computational algorithms.
• Parallel optimization algorithms.
• Applications of optimization to artificial intelligence, especially machine learning.

Member of Editorial Boards

• SIAM Journal on Optimization (from 2010)
• Mathematical Programming, Series A (since 2005)
• Optimization Methods and Software (since 2002)

Books and Edited Volumes

1.   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).
    
2.   Optimization, Volume 2: Computational Methods.
   Alexey Izmailov and Mikhail Solodov.
   Rio de Janeiro, Brazil, 2007.
   (In Portuguese, 458 pages, ISBN: 978-85-244-0268-5).
   [ Prefácio ] [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, ISBN: 978-85-244-0238-8 (In Portuguese, 270 pages).
   [ Prefácio ] [Conteúdo] [Compras]
    
4.   Optimization Methods and Software, Vol. 19, October 2004. [Contents]
   (11 papers, dedicated to Olvi Mangasarian).
   M.C. Ferris and M.V. Solodov (Editors).
    
5.   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.   Sharp primal superlinear convergence results for some Newtonian methods for constrained optimization. [ pdf ]
   D. Fernández, A.F. Izmailov, and M.V. Solodov
   November 2009.
    
2.   Stabilized SQP revisted. [ pdf ]
   A.F. Izmailov and M.V. Solodov
   September 2009.
    
3.   A truncated SQP method based on inexact interior-point solutions of subproblems. [ pdf ]
   A.F. Izmailov and M.V. Solodov
   May 2009 (revised November 2009).
    
4.   The hybrid proximal decomposition method applied to the computation of a Nash equillibrium for hydrothermal electricity markets. [ pdf ]
   L.A. Parente, P.A. Lotito, F.J. Mayorano, A.J. Rubiales, and M.V. Solodov
   November 2008.
    
5.   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
   October 2008 (revised March 2009).
   Computational Optimization and Applications, to appear.
    
6.   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.
    
7.   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.
    
8.   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
   March 2008 (revised February 2009).
   Mathematical Programming, to appear.
    
9.   Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems. [ pdf ] [ doi ]
   Damián Fernández and Mikhail Solodov
   IMPA preprint A568, November 2007 (revised September 2008).
   Mathematical Programming, to appear.
    
10.   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)
     
11.   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.
     
12.   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.
     
13.   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.
     
14.   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.
     
15.   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.
     
16.   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.
     
17.   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.
     
18.   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
     
19.   An explicit descent method for bilevel convex optimization. [ pdf ]
    Mikhail Solodov
    Journal of Convex Analysis 14 (2007), 227-238.
     
20.   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.
     
21.   A note on error estimates for some interior penalty methods. [ pdf ]
    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.
     
22.   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.
     
23.   Numerical results for a globalized active-set Newton method for mixed complementarity problems. [ pdf ]
    A.N. Daryina, A.F. Izmailov and M.V. Solodov
    Computational and Applied Mathematics 24 (2005), 293-316.
     
24.   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.
     
25.   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.
     
26.   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.
     
27.   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.
     
28.   On the sequential quadratically constrained quadratic programming methods. [ pdf ] [ doi ]
    M.V. Solodov
    Mathematics of Operations Research 29 (2004), 64-79.
     
29.   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.
     
30.   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.
     
31.   Merit functions and error bounds for generalized variational inequalities. [ pdf ] [ doi ]
    M.V. Solodov
    Journal of Mathematical Analysis and Applications 287 (2003), 405-414.
     
32.   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.
     
33.   Convergence rate analysis of iterative algorithms for solving variational inequality problems. [ pdf ] [ doi ]
    M.V. Solodov
    Mathematical Programming 96 (2003), 513-528.
     
34.   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.
     
35.   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.
     
36.   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.
     
37.   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.
     
38.   Parallel variable distribution for constrained optimization. [ pdf ] [ doi ]
    C.A. Sagastizábal and M.V. Solodov
    Computational Optimization and Applications 22 (2002), 111-131.
     
39.   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.
     
40.   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.
     
41.   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.
     
42.   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.
     
43.   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.
     
44.   Implicit Lagrangian. [ ps ]
    M.V. Solodov
    An invited article for the Encyclopedia of Optimization, C. Floudas and P. Pardalos (editors),
    Kluwer Academic Publishers, 2001.
     
45.   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.
     
46.   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.
     
47.   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.
     
48.   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.
     
49.   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.
     
50.   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.
     
51.   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.
     
52.   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.
     
53.   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.
     
54.   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.
     
55.   Some optimization reformulations of the extended linear complementarity problem. [ pdf ] [ doi ]
    M.V. Solodov
    Computational Optimization and Applications 13 (1999), 187-200.
     
56.   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.
     
57.   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.
     
58.   A hybrid projection-proximal point algorithm. [ ps ]
    M.V. Solodov and B.F. Svaiter
    Journal of Convex Analysis 6 (1999), 59-70.
     
59.   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.
     
60.   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.
     
61.   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.
     
62.   On the convergence of constrained parallel variable distribution algorithms. [ pdf ] [ doi ]
    M.V. Solodov
    SIAM Journal on Optimization 8 (1998), 187-196.
     
63.   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.
     
64.   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.
     
65.   Incremental gradient algorithms with stepsizes bounded away from zero. [ pdf ] [ doi ]
    M.V. Solodov
    Computational Optimization and Applications 11 (1998), 23-35.
     
66.   Convergence analysis of perturbed feasible descent methods. [ pdf ] [ doi ]
    M.V. Solodov
    Journal of Optimization Theory and Applications 93 (1997), 337-353.
     
67.   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.
     
68.   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.
     
69.   Newton-type methods with generalized distances for constrained optimization. [ ps ] [ doi ]
    A.N. Iusem and M.V. Solodov
    Optimization 41 (1997), 257-278.
     
70.   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.
     
71.   New inexact parallel variable distribution algorithms. [ pdf ] [ doi ]
    M.V. Solodov
    Computational Optimization and Applications 7 (1997), 165-182.
     
72.   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.
     
73.   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.
     
74.   Serial and parallel backpropagation convergence via nonmonotone perturbed minimization. [ ps ]
    O.L. Mangasarian and M.V. Solodov
    Optimization Methods and Software 4 (1994), 103-116.
     
75.   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.
     
76.   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.
     
77.   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.