The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasonin...

The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algo...

We consider the problem of separating two sets of points in an <i>n</i>-dimensional real space with a (hyper)plane that minimizes the sum of <i>L<sub>p</sub...

<p> This paper introduces the Mesh Adaptive Direct Search (MADS) class of algorithms for nonlinear optimization. MADS extends the Generalized Pattern Searc...

A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the Audet-De...

Linear mixed 0-1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (<i>BLP</i>) problems. We exploit the...

Bimatrix and polymatrix games are expressed as parametric linear 0-1 programs. This leads to an algorithm for complete enumeration of their extreme equilibri...

Goal Programming with fractional objectives can be reduced to mathematical programming with a linear objective under linear and quadratic constraints, thus...

This paper answers a query of S. Vincze (Acta Univ. Szeged, Sect. Sci. Math. 12 A (1950) 136-142): find the convex octagon with unit-length sides and minim...

This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a f...

Cet article propose un modèle d’optimisation des stratégies de maintenance pour une meilleure intégration dans un plan de production préétabli. Le modèle est...

We present an exact algorithm and three applications of nonconvex quadratically constrained quadratic programming. First, we consider the pooling problem fro...

The convergence theory of generalized pattern search algorithms for unconstrained optimization guarantees under mild conditions that the method produces a li...

The pooling problem, which is fundamental to the petroleum industry, describes a situation where products possessing different attribute qualities are mixed...

A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses th...

This paper describes a method for evaluating the kinetic constants in a rate expression for catalytic combustion applications using experimental light-off c...

This paper contains a new convergence analysis for the Lewis and Torczon GPS class of pattern search methods for linearly constrained optimization. The ana...

Thrackleation of graphs and global optimization for quadratically constrained quadratic programming are used to find the octagon with unit diameter and larg...

In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperature...

The set of equilibrium points of a bimatrix game is the union of polytopes that are not necessarily disjoint. Knowledge of the vertices of these polytopes ...