The paper answers the three distinct questions of maximizing the perimeter, diameter and area of equilateral unit-width convex polygons. The solution to each...

A positive basis is a minimal set of vectors whose nonnegative linear combinations span the entire space R<i>ⁿ</i>. Interest in positive bases wa...

In this paper we establish the definition of the <i>set of &epsilon;-proper equilibria</i> of a bimatrix game. We define a 0-1 mixed quadratic program to ge...

The main goal of this paper is to bring a contribution in order to facilitate automatic refinement of Bimatrix Game Nash extreme equilibria. We show how maxi...

We introduce the OPAL framework in which the identification of good algorithmic parameters is interpreted as a black box optimization problem whose variables...

Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realist...

Relationships between the diameter of a set of <i>n</i> points in the plane at mutual distance at least one, the diameter of an equilateral <i>n</i>-gon and ...

This work analyzes constrained black box optimization in which the functions defining the problem are periodic with respect to some or all the variables. We ...

This work studies multi-objective optimization <i>(MOP)</i> of nonsmooth functions subject to general constraints. We first present definitions and optimalit...

A recent paper of Tuy and Hoai-Phuong published in <i>JOGO</i> (2007) 37:557--569 observes that there are errors in the reformulation of a signomial geometr...

<p>The class of Mesh Adaptive Direct Search (MADS) algorithms is designed for the optimization of constrained black-box problems. The purpose of this paper i...

A polygon is said to be <i>simple</i> if the only points of the plane belonging to two of its edges are its vertices. We answer the question of finding, ...

The hexagon and heptagon with unit diameter and maximum sum of Euclidean distances between vertices are determined by enumerating diameter configurations, an...

The purpose of this paper is to introduce a new way of choosing directions for the Mesh Adaptive Direct Search (MADS) class of algorithms. The advantages of...

We propose a new approach to solve the multi-objective portfolio selection problem in the presence of skewness. The selection of efficient portfolios require...

In previous work, bimatrix games were expressed as parametric linear mixed 0-1 programs and the <img src="/cgi-bin/mimetex.cgi?{\rm E}_\chi">MIP algorithm w...

Consider a convex polygon <i>V_n</i> with <i>n</i> sides, perimeter <i>P_n</i>, diameter <i>D_n</i>, area <i>A_n</i>...

This paper describes a Parallel Space Decomposition (PSD) technique for the Mesh Adaptive Direct Search (MADS) algorithm. MADS extends Generalized Pattern ...

In previous work, the generalized pattern search (GPS) algorithm for linearly constrained (continuous) optimization was extended to mixed variable problems...

We propose a new algorithm for general constrained derivative-free optimization. As in most methods, constraint violations are aggregated into a single con...