Interests:
optimization  mathematical programming  operations research
Research Summary

Newton and Newtonrelated algorithms for optimization and variational problems
(especially, under weakerthanstandard assumptions).

Augmented Lagrangian and related techniques.

Decomposition.

Nonsmooth optimization, especially (but not only) bundle methods.

Inexact proximalpointrelated 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 errorstability analysis of computational algorithms.

Parallel optimization algorithms (former interest).

Applications of optimization to
machine learning (former interest).
Member of Editorial Boards
PUBLICATIONS
Books

NewtonType 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]

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: 9788524404542).
[ Prefácio e Conteúdo]
[Compras]

Optimization, Volume 1: Optimality Conditions, Elements of
Convex Analysis and Duality.
Alexey Izmailov and Mikhail Solodov.
Rio de Janeiro, Brazil, 2005. ISBN: 8524402385.
Second Edition 2009, Third Edition 2014, Fourth Edition 2020. ISBN: 9786599052804
(In Portuguese, 274 pages).
[ Prefácio e Conteúdo]
[Compras]

Numerical Methods of Optimization.
A.F. Izmailov and M.V. Solodov.
Fizmatlit/Nauka,
Moscow, Russia, 2003, ISBN: 5922100459.
Second Edition 2008. ISBN: 9785922109758
(In Russian, 320 pages).
[ Preface and Contents ]
Edited Volumes

Mathematical Programming, Series B, Vol. 1982, April 2023.
[Contents]
(special issue on Hierarchical Optimization).
Kristin P. Bennett, Michael C. Ferris, JongShi Pang, Mikhail V. Solodov,
and Stephen J. Wright (Editors).

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).

Optimization Methods and Software, Vol. 19, October 2004.
[Contents]
(dedicated to Olvi Mangasarian).
M.C. Ferris and M.V. Solodov (Editors).
Research Articles

A general perturbed Newtonian framework and critical solutions of nonlinear equations.
[ pdf ]
A. Izmailov and M. Solodov
July 2024.

The LevenbergMarquardt method:
An overview of modern convergence theories and more.
[ doi ]
[ pdf ]
A. Fischer, A. Izmailov, and M. Solodov
Computational Optimization and Applications 89 (2024), 3367.

On local behavior of Newtontype methods near critical
solutions of constrained equations.
[ doi ]
[ pdf ]
A. Izmailov and M. Solodov
Journal of Optimization Theory and Applications, 2024.

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), 89115.

Convergence rate estimates for penalty methods revisited.
[ doi ]
[ pdf ]
A. Izmailov and M. Solodov
Computational Optimization and Applications 85 (2023), 973992.

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), 17671796.

Profit sharing mechanisms in multiowned cascaded hydrosystems.
[ pdf ]
[ doi ]
Pedro Borges, Claudia Sagastizábal, Mikhail Solodov, Leo Liberti, and
Claudia D'Ambrosio
Optimization and Engineering 24 (2023), 20052043.

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), 787820.

A distributionallyambiguous twostage 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), 484504.

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), 491522.

A regularized smoothing method for fully parameterized convex problems
with applications to convex and nonconvex twostage stochastic programming.
[ pdf ]
[ doi ]
Pedro Borges, Claudia Sagastizábal, and Mikhail Solodov
Mathematical Programming 189 (2021), 117149.

Decomposition algorithms for some deterministic and twostage stochastic
singleleader multifollower games.
[ pdf ]
[ doi ]
Pedro Borges, Claudia Sagastizábal, and Mikhail Solodov
Computational Optimization and Applications 78 (2021), 675704.

Unit stepsize for the Newton method close to critical solutions.
[ pdf ]
[ doi ]
A. Fischer, A. Izmailov, and M. Solodov
Mathematical Programming 187 (2021), 697721.

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), 273286.

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), 935959.

Bundle methods for inexact data.
[ pdf ]
[ doi ]
Welington de Oliveira and Mikhail Solodov
In Numerical Nonsmooth Optimization  State of the Art Algorithms, pages 417459.
A. Bagirov, M. Gaudioso, N. Karmitsa, M. Mäakelä and S. Taheri (editors).
Springer, 2020.

On the cost of solving augmented Lagrangian subproblems.
[ pdf ]
[ doi ]
D. Fernández and M. Solodov
Mathematical Programming 182 (2020), 3755.

Multiplier stabilization applied to twostage stochastic programs.
[ pdf ]
[ doi ]
Clara Lage, Claudia Sagastizábal, and Mikhail Solodov
Journal of Optimization Theory and Applications 183 (2019), 158178.

A globally convergent LevenbergMarquardt method for
equalityconstrained optimization.
[ pdf ]
[ doi ]
A.F. Izmailov, M.V. Solodov, and E.I. Uskov
Computational Optimization and Applications 72 (2019), 215239.

Subdifferential enlargements
and continuity properties of the
VUdecomposition 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. 5587, 2019. Birkhauser, Cham.

Local attractors of Newtontype 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), 140169.

Critical solutions of nonlinear equations: Local attraction for Newtontype methods.
[ pdf ]
[ doi ]
A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
Mathematical Programming 167 (2018), 355379.

Critical solutions of nonlinear equations: Stability issues.
[ pdf ]
[ doi ]
A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
Mathematical Programming 168 (2018), 475507.

A globally convergent LPNewton 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), 325349.

A doubly stabilized bundle method for nonsmooth convex optimization.
[ pdf ]
[ doi ]
Welington de Oliveira and Mikhail Solodov
Mathematical Programming 156 (2016), 125159.

A globally convergent LPNewton method.
[ pdf ]
[ doi ]
A. Fischer, M. Herrich, A. Izmailov, and M. Solodov
SIAM Journal on Optimization 26 (2016), 20122033.

An approximation scheme for a class of riskaverse stochastic
equilibrium problems.
[ pdf ]
[ doi ]
Juan Pablo Luna, Claudia Sagastizábal, and Mikhail Solodov
Mathematical Programming 157 (2016), 451481.

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), 11111131.

Convergence conditions for Newtontype 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), 425459.

Globalizing stabilized sequential quadratic programming method
by smooth primaldual exact penalty function.
[ pdf ]
[ doi ]
A.F. Izmailov, M.V. Solodov, and E.I. Uskov
Journal of Optimization Theory and Applications 169 (2016), 148178.

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), 128.

Newtontype methods: A broader view.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Journal of Optimization Theory and Applications 164 (2015), 577620.

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), 126.
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), 4852.
[ pdf ]
[ doi ]

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), 405429.

Some compositestep 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), 461477.

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), 111140.

Complementarity and gametheoretical models for equilibria in energy markets:
deterministic and riskaverse 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. 237264, 2014.

On error bounds and Newtontype methods for
generalized Nash equilibrium problems.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Computational Optimization and Applications 59 (2014), 201218.

A class of DantzigWolfe type decomposition methods for
variational inequality problems.
[ pdf ]
[ doi ]
Juan Pablo Luna, Claudia Sagastizábal, and Mikhail Solodov
Mathematical Programming 143 (2014), 177209.

Stabilized sequential quadratic programming: A survey.
[ pdf ]
[ doi ]
D. Fernández and M. Solodov
Pesquisa Operacional 34 (2014), 463479
(special issue on Nonlinear Programming).

A note on upper Lipschitz stability, error bounds, and
critical multipliers for Lipschitzcontinuous KKT systems.
[ pdf ]
[ doi ]
A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
Mathematical Programming 142 (2013), 591604.

The JosephyNewton method for
semismooth generalized equations and semismooth SQP for optimization.
[ pdf ]
[ doi ]
A.F. Izmailov, A.S. Kurennoy, and M.V. Solodov
SetValued and Variational Analysis 21 (2013), 1745.

Solving net constrained hydrothermal NashCournot 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), 301322.
(special issue on Equilibrium Optimization).

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), 15791606.

Local convergence of exact and inexact augmented Lagrangian methods
under the secondorder sufficient optimality condition.
[ pdf ]
[ doi ]
D. Fernández and M. Solodov
SIAM Journal on Optimization 22 (2012), 384407.

Solving generation expansion planning problems with environmental constraints
by a bundle method.
[ pdf ]
[ doi ]
Claudia Sagastizábal and Mikhail Solodov
Computational Management Science 9 (2012), 163182.

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), 199221.

Stabilized SQP revisited.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Mathematical Programming 133 (2012), 93120.

Semismooth SQP method for equalityconstrained
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), 847872.

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), 277302.

On attraction of linearly constrained Lagrangian methods and
of stabilized and quasiNewton SQP methods to critical multipliers.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Mathematical Programming 126 (2011), 231257.

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.

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), 33123334.

Inexact JosephyNewton 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), 347368.

A truncated SQP method based on inexact interiorpoint
solutions of subproblems.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
SIAM Journal on Optimization 20 (2010), 25842613.

Stabilized sequential quadratic programming for
optimization and a stabilized Newtontype method for
variational problems.
[ pdf ]
[ doi ]
Damián Fernández and Mikhail Solodov
Mathematical Programming 125 (2010), 4773.

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), 820840.

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), 857880.

Examples of dual behaviour of Newtontype methods on
optimization problems with degenerate constraints.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Computational Optimization and Applications 42 (2009), 231264.
[ 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)

A survey on dual behavior of Newtontype 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. 157174.

Global convergence of an SQP method without boundedness
assumptions on any of the iterative sequences.
[ pdf ]
[ doi ]
Mikhail Solodov
Mathematical Programming 118 (2009), 112.

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), 501532.

On attraction of Newtontype iterates to
multipliers violating secondorder sufficiency conditions.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Mathematical Programming 117 (2009), 271304.

A bundlefilter method for nonsmooth convex
constrained optimization.
[ pdf ]
[ doi ]
E. Karas, A. Ribeiro, C. Sagastizábal, and M. Solodov
Mathematical Programming 116 (2009), 297320.

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), 240260.

On local convergence of sequential quadraticallyconstrained
quadraticprogramming type methods,
with an extension to variational problems.
[ pdf ]
[ doi ]
Damián Fernández and Mikhail Solodov
Computational Optimization and Applications 39 (2008), 143160.

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), 10031027.

A bundle method for a class of bilevel nonsmooth convex
minimization problems.
[ pdf ]
[ doi ]
Mikhail Solodov
SIAM Journal on Optimization 18 (2007), 242259.
[ genbi.m ] Matlab generator of problems
described in this paper

An explicit descent method for bilevel convex optimization.
[ pdf ]
Mikhail Solodov
Journal of Convex Analysis 14 (2007), 227238.

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), 575589.

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, SpringerVerlag Berlin Heidelberg, 2006, pp. 133145.

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), 146169.

Numerical results for a globalized activeset Newton method
for mixed complementarity problems.
[ pdf ]
[ doi ]
A.N. Daryina, A.F. Izmailov, and M.V. Solodov
Computational and Applied Mathematics 24 (2005), 293316.

A note on solution sensitivity for KarushKuhnTucker systems.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Mathematical Methods of Operations Research 61 (2005), 347363.

A class of activeset 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), 409429.

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), 557575.

Newtontype methods for optimization problems without
constraint qualifications.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
SIAM Journal on Optimization 15 (2004), 210228.

On the sequential quadratically constrained quadratic
programming methods.
[ pdf ]
[ doi ]
M.V. Solodov
Mathematics of Operations Research 29 (2004), 6479.

On approximations with finite precision in bundle methods for
nonsmooth optimization.
[ pdf ]
[ doi ]
M.V. Solodov
Journal of Optimization Theory and Applications
119 (2003), 151165.

KarushKuhnTucker systems: regularity conditions, error bounds
and a class of Newtontype methods.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Mathematical Programming 95 (2003), 631650.

Merit functions and error bounds for generalized variational
inequalities.
[ pdf ]
[ doi ]
M.V. Solodov
Journal of Mathematical Analysis and Applications 287 (2003),
405414.

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. 6382.

Convergence rate analysis of iterative algorithms for
solving variational inequality problems.
[ pdf ]
[ doi ]
M.V. Solodov
Mathematical Programming 96 (2003), 513528.

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), 386405.

A new proximalbased globalization strategy for the JosephyNewton
method for variational inequalities.
[ pdf ]
[ doi ]
M.V. Solodov and B.F. Svaiter
Optimization Methods and Software 17 (2002), 965983.

The theory of 2regularity 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), 614635.

On optimality conditions for coneconstrained optimization.
A.F. Izmailov and M.V. Solodov
In Proceedings of the 41st IEEE Conference on Decision and
Control, Omnipress, 2002.

Parallel variable distribution for constrained optimization.
[ pdf ]
[ doi ]
C.A. Sagastizábal and M.V. Solodov
Computational Optimization and Applications
22 (2002), 111131.

Complementarity constraint qualification via the theory of
2regularity.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
SIAM Journal on Optimization 13 (2002), 368385.

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),
10131035.

Error bounds for 2regular mappings with Lipschitzian derivatives
and their applications.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
Mathematical Programming 89 (2001), 413435.

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. 297315.

Optimality conditions for irregular inequalityconstrained problems.
[ pdf ]
[ doi ]
A.F. Izmailov and M.V. Solodov
SIAM Journal on Control and Optimization 40 (2001/2002), 12801295.

Implicit Lagrangian.
[ ps ]
M.V. Solodov
Encyclopedia of Optimization,
C. Floudas and P. Pardalos (editors),
Kluwer Academic Publishers, 2001.

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. 441455.

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), 371389.

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. 415427.

Some methods based on the Dgap function for solving monotone variational
inequalities.
[ pdf ]
[ doi ]
M.V. Solodov and P. Tseng
Computational Optimization and Applications 17 (2000), 255277.

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), 214230.

A truly globally convergent Newtontype method for the monotone
nonlinear complementarity problem.
[ pdf ]
[ doi ]
M.V. Solodov and B.F. Svaiter
SIAM Journal on Optimization 10 (2000), 605625.

The theory of 2regularity 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. 2650.

Forcing strong convergence of proximal point iterations in a Hilbert
space.
[ pdf ]
[ doi ]
M.V. Solodov and B.F. Svaiter
Mathematical Programming 87 (2000), 189202.

A linearly convergent derivativefree descent method for strongly
monotone complementarity problems.
[ pdf ]
[ doi ]
O.L. Mangasarian and M.V. Solodov
Computational Optimization and Applications 14 (1999), 516.

A hybrid approximate extragradientproximal point algorithm using
the enlargement of a maximal monotone operator.
[ pdf ]
[ doi ]
M.V. Solodov and B.F. Svaiter
SetValued Analysis 7 (1999), 323345.

Some optimization reformulations of the extended linear complementarity
problem.
[ pdf ]
[ doi ]
M.V. Solodov
Computational Optimization and Applications 13 (1999), 187200.

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), 765776.

Parallel constrained optimization via distribution of variables.
C.A. Sagastizábal and M.V. Solodov
In Lecture Notes in Computer Science, Vol. 1685, pp.
11121119,
P. Amestoy et al. (editors),
SpringerVerlag, 1999.

A hybrid projectionproximal point algorithm.
[ pdf ]
M.V. Solodov and B.F. Svaiter
Journal of Convex Analysis 6 (1999), 5970.

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. 13071314.

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. 355369.

A projectiontype method for pseudomonotone variational inequality
problems.
M.V. Solodov and B.F. Svaiter
In Proceedings of the 38th IEEE Conference on Decision and
Control, Omnipress, 1999, pp. 25692574.

On the convergence of constrained parallel variable distribution
algorithms.
[ pdf ]
[ doi ]
M.V. Solodov
SIAM Journal on Optimization 8 (1998), 187196.

Error stability properties of generalized gradienttype algorithms.
[ pdf ]
[ doi ]
M.V. Solodov and S.K. Zavriev
Journal of Optimization Theory and Applications 98 (1998), 663680.

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), 2335.

Incremental gradient algorithms with stepsizes bounded away from
zero.
[ pdf ]
[ doi ]
M.V. Solodov
Computational Optimization and Applications 11 (1998), 2335.

Convergence analysis of perturbed feasible descent methods.
[ pdf ]
[ doi ]
M.V. Solodov
Journal of Optimization Theory and Applications 93 (1997), 337353.

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), 235255.

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),
265275.

Newtontype methods with generalized distances for constrained
optimization.
[ ps ]
[ doi ]
A.N. Iusem and M.V. Solodov
Optimization 41 (1997), 257278.

Stationary points of bound constrained minimization reformulations
of complementarity problems.
[ pdf ]
[ doi ]
M.V. Solodov
Journal of Optimization Theory and Applications 94 (1997), 449467.

New inexact parallel variable distribution algorithms.
[ pdf ]
[ doi ]
M.V. Solodov
Computational Optimization and Applications 7 (1997), 165182.

Modified projectiontype methods for monotone variational inequalities.
[ ps ]
[ doi ]
M.V. Solodov and P. Tseng
SIAM Journal on Control and Optimization 34 (1996), 18141830.

Nonmonotone and Perturbed Optimization, Ph.D. Dissertation.
M.V. Solodov
Mathematical Programming Technical Report 9513,
Computer Sciences Department, University of Wisconsin,
1210 West Dayton Street, Madison, Wisconsin 53706, U.S.A., August 1995.

Serial and parallel backpropagation convergence via nonmonotone
perturbed minimization.
[ ps ]
[ doi ]
O.L. Mangasarian and M.V. Solodov
Optimization Methods and Software 4 (1994), 103116.

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), 880892.

Backpropagation convergence via deterministic perturbed minimization.
[ ps ]
O.L. Mangasarian and M.V. Solodov
In Advances in Neural Information Processing Systems ,
Vol. 6, pp. 383390,
J.D. Cowan, G. Tesauro and J. Alspector (editors), Morgan Kaufmann
Publishers, 1994.

Nonlinear complementarity as unconstrained and constrained minimization.
[ pdf ]
[ doi ]
O.L. Mangasarian and M.V. Solodov
Mathematical Programming 62 (1993), 277297.
Last Updated: July 2024.
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.
