In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obta...

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

We present a proximal point method to solve multiobjective problems based on the scalarization for maps. We build a family of a convex scalar strict representation of a convex map F with respect to the lexicographic order on R and we add a variant of the logarithmquadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced on the quadratic term and ...

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it...

In this paper, we presented a logarithmic-quadratic proximal alternating direction method for structured variational inequalities. The method generates the new iterate by searching the optimal step size along the descent direction. Global convergence of the new method is proved under certain assumptions.

In this paper, we proposed a logarithmic-quadratic proximal alternating direction method for structured variational inequalities. The new iterate is obtained by a convex combination of the previous point and the one generated by a projection-type method along a new descent direction. Global convergence of the new method is proved under certain assumptions. We also reported some numerical result...

Two inexact versions of a Bregman-function-based proximal method for nding a zero of a maximal monotone operator, suggested in [4] and [3], are considered. For a wide class of Bregman functions convergence of these methods is proved under an essentially weaker condition on the sequence of errors than in the original papers. Also the error criterion of a logarithmic-quadratic proximal method, de...

In this paper, we proposed a modified Logarithmic-Quadratic Proximal (LQP) method [Auslender et al.: Comput. Optim. Appl. 12, 31–40 (1999)] for solving variational inequalities problems. We solved the problem approximately, with constructive accuracy criterion. We show that the method is globally convergence under that the operator is pseudomonotone which is weaker than the monotonicity and the...

This paper presents an inexact proximal method for solving monotone variational inequality problems with a given separable structure. The proposed algorithm is natural extension of the Proximal Multiplier Algorithm Distances (PMAPD) by Sarmiento et al . [ Optimization 65 (2016) 501–537], which unified works Chen and Teboulle (PCPM method), Kyono Fukushima (NPCPMM) developed convex programs part...