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We propose a new projection algorithm for solving the variational inequality problem, where the underlying function is continuous and satisfies a certain generalized monotonicity assumption (e.g., itâ€¦ (More)

We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, anâ€¦ (More)

- Olvi L. Mangasarian, Mikhail V. Solodov
- Math. Program.
- 1993

The nonlinear complementarity problem is cast as an unconstrained minimization problem that is obtained from an augmented Lagrangian formulation. The dimensionality of the unconstrained problem isâ€¦ (More)

- Mikhail V. Solodov, Benar Fux Svaiter
- Math. Oper. Res.
- 2000

We present a new Bregman-function-based algorithm which is a modi6cation of the generalized proximal point method for solving the variational inequality problem with a maximal monotone operator. Theâ€¦ (More)

- Mikhail V. Solodov, Benar Fux Svaiter
- Math. Program.
- 2000

This paper concerns with convergence properties of the classical proximal point algorithm for nding zeroes of maximal monotone operators in an innnite-dimensional Hilbert space. It is well known thatâ€¦ (More)

- Alexey F. Izmailov, Mikhail V. Solodov
- Comp. Opt. and Appl.
- 2010

We propose and analyze a perturbed version of the classical Josephy-Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standardâ€¦ (More)

- DamiÃ¡n R. FernÃ¡ndez, Mikhail V. Solodov
- Math. Program.
- 2010

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimizationâ€¦ (More)

- Mikhail V. Solodov, Benar Fux Svaiter
- Math. Program.
- 2000

We study various error measures for approximate solution of proximal point regularizations of the variational inequality problem, and of the closely related problem of finding a zero of a maximalâ€¦ (More)

- Alexey F. Izmailov, Mikhail V. Solodov
- Math. Program.
- 2001

We obtain local estimates of the distance to a set defined by equality constraints under assumptions which are weaker than those previously used in the literature. Specifically, we assume that theâ€¦ (More)

- Mikhail V. Solodov
- Comp. Opt. and Appl.
- 1998

We consider the class of incremental gradient methods for minimizing a sum of continuously differentiable functions. An important novel feature of our analysis is that the stepsizes are kept boundedâ€¦ (More)