This paper presents a new inexact proximal method for solving monotone variational inequality problems with a given separable structure. The resulting method combines the recent proximal distances theory introduced by Auslender and Teboulle (2006) with a decomposition method given by Chen and Teboulle that was proposed to solve convex optimization problems. This method extends and generalizes p...

In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer suitable proximal parameter to each of first grouped subproblems, develop partial LQP-based Alternating Direction Method Multipliers (ADMM-LQP). The dual variable is updated twice relatively larger stepsizes tha...

It was recently shown that the alternating direction method with logarithmicquadratic proximal regularization can yield an efficient algorithm for a class of variational inequalities with separable structures. This paper further shows the O(1/t) convergence rate for this kind of algorithms. Both the cases with a simple or general Glowinski’s relaxation factor are discussed.

Recently, Gregório and Oliveira developed a proximal point scalarization method (applied to multiobjective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this work we propose a variation of this method, taking into account the regularization with logarithm and quasi-distance, wher...

In the literature, the combination of the alternating direction method of multipliers (ADMM) with the logarithmic-quadratic proximal (LQP) regularization has been proved to be convergent and its worst-case convergence rate in the ergodic sense has been established. In this paper, we focus on a convex minimization model and consider an inexact version of the combination of the ADMM with the LQP ...

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the quadratic program is the relaxation of a binary quadratic problem.

We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves sequence of inner subproblems which can be enforced to strongly convex and therefore admit unique solution. The resulting steps are shown equivalent inexact point iterations extended-real-valued cost function, allows for fairly simple analysis where convergence s...