This article deals with a study of the MPEC problem based on a reformulation to a DC problem (Difference of Convex functions). This reformulation is obtained by a partial penalization of the constraints. In this article we prove that a classical optimality condition for a DC program, if a constraint qualification is satisfied for MPEC, … Read more
We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility by shedding load at demand nodes, but doing so in a way … Read more
A lot of real-world optimization models comprise nonconvex and nonlinear as well as nonsmooth functions leading to very hard classes of optimization models. In this article a new interior-point method for the special but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under … Read more
We propose a copositive reformulation of the mixed-integer fractional quadratic problem (MIFQP) under general linear constraints. This problem class arises naturally in many applications, e.g., for optimizing communication or social networks, or studying game theory problems arising from genetics. It includes several APX-hard subclasses: the maximum cut problem, the $k$-densest subgraph problem and several of … Read more
The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point … Read more
In a recent Math. Program. paper, Eckstein and Silva proposed a new error criterion for the approximate solutions of augmented Lagrangian subproblems. Based on a saddle-point formulation of the primal and dual problems, they proved that dual sequences generated by augmented Lagrangians under this error criterion are bounded and that theirs limit points are dual … Read more
Inexact Restoration methods have been proved to be effective to solve constrained optimization problems in which some structure of the feasible set induces a natural way of recovering feasibility from arbitrary infeasible points. Sometimes natural ways of dealing with minimization over tangent approximations of the feasible set are also employed. A recent paper [N. Banihashemi … Read more
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. Our framework is very flexible and includes both fully parallel Jacobi schemes and Gauss-Seidel (i.e., sequential) ones, as … Read more
Blackbox optimization deals with situations in which the objective function and constraints are typically computed by launching a time-consuming computer sim- ulation. The subject of this work is the Mesh Adaptive Direct Search (MADS) class of algorithms for blackbox optimization. We propose a way to dynamically scale the mesh, which is the discrete spatial structure … Read more
This paper shows how, in a quasi metric space, an inexact proximal algorithm with a generalized perturbation term appears to be a nice tool for Behavioral Sciences (Psychology, Economics, Management, Game theory,…). More precisely, the new perturbation term represents an index of resistance to change, defined as a “curved enough” function of the quasi distance … Read more