On Blocking and Anti-Blocking Polyhedra in Infinite Dimensions

We consider the natural generalizations of blocking and anti-blocking polyhedra in infinite dimensions, and study issues related to duality and integrality of extreme points for these sets. Using appropriate finite truncations, we give conditions under which complementary slackness holds for primal-dual pairs of the infi nite linear programming problems associated with infi nite blocking and anti-blocking polyhedra. … Read more

A semidefinite programming hierarchy for packing problems in discrete geometry

Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for the maximal size of an independent set is to use Lasserre’s semidefinite programming hierarchy. We generalize … Read more

Computation of Stochastic Nash Equilibrium via Variable Sample Distributed Methods

In this paper, we propose a variable sample distributed algorithm for the computation of stochastic Nash equilibrium in which the objective functions are replaced, at each iteration, by sample average approximations. We investigate the contraction mapping properties of the variable sample distributed algorithm and show that the accuracy of estimators yielded in the algorithms to … Read more

Minimum concave cost flows in capacitated grid networks

We study the minimum concave cost flow problem over a two-dimensional grid network (CFG), where one dimension represents time ($1\le t\le T$) and the other dimension represents echelons ($1\le l\le L$). The concave function over each arc is given by a value oracle. We give a polynomial-time algorithm for finding the optimal solution when the … Read more

Narrowing the difficulty gap for the Celis-Dennis-Tapia problem

We study the {\em Celis-Dennis-Tapia (CDT) problem}: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is not yet fully understood. Our main objective in this paper is to narrow the difficulty gap that … Read more

Differentiability properties of metric projections onto convex sets

It is known that directional differentiability of metric projection onto a closed convex set in a finite dimensional space is not guaranteed. In this paper we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems. Article Download View Differentiability … Read more

Derivative-free Robust Optimization for Circuit Design

In this paper, we introduce a framework for derivative-free robust optimization based on the use of an efficient derivative-free optimization routine for mixed integer nonlinear problems. The proposed framework is employed to find a robust optimal design of a particular integrated circuit (namely a DC-DC converter commonly used in portable electronic devices). The proposed robust … Read more

A Derivative-Free Algorithm for Constrained Global Optimization based on Exact Penalty Functions

Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization technique for minimizing a non-differentiable exact penalty func- tion for given values of the penalty parameter, and an automatic updating of the penalty parameter … Read more

Multimaterial topology optimization by volume constrained Allen-Cahn system and regularized projected steepest descent method

A new computational algorithm is introduced in the present study to solve multimaterial topology optimization problems. It is based on the penalization of the objective functional by the multiphase volume constrained Cahn-Hilliard energy functional. The update procedure is based on the gradient flow of the objective functional by a fractional step projected steepest descent method. … Read more

Modeling with Metaconstraints and Semantic Typing of Variables

Recent research in hybrid optimization shows that a combination of technologies that exploits their complementary strengths can significantly speed up computation. The use of high-level metaconstraints in the problem formulation can achieve a substantial share of these computational gains by better communicating problem structure to the solver. During the solution process, however, metaconstraints give rise … Read more