This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm, which extends the Generalized Pattern Search (GPS) algorithm, with th...

We consider the problem of separating two sets of points in an n-dimensional real space with a (hyper)plane that minimizes the sum of <i>L</i>₂-n...

This work deals with bound constrained multiobjective optimization (<i>MOP</i>) of nonsmooth functions for problems in which the structure of the objective ...

This paper presents two new results on the enumeration of all extreme equilibria of the sequence form of a two person extensive game. The sequential form of...

In this paper, the general problem of chemical process optimization defined by a computer simulation is formulated. It is generally a nonlinear, non-convex,...

The value <img src="/cgi-bin/mimetex.cgi?\frac{1}{2n} \cot\left( \frac{\pi}{2n}\right)"> is shown to be an upper bound on the width of any <i>n</i>-sided p...

From the pentagon onwards, the area of the regular convex polygon with <i>n</i> sides and unit diameter is greater for each odd number <i>n</i> than for the...

In [<i>SIAM J. Optim.</i>, 17 (2006), pp. 188–217] Audet and Dennis proposed the class of <i>mesh adaptive direct search algorithms</i> (MADS) for minimizat...

This work shows how disjunctive cuts can be generated for a bilevel linear programming problem (<i>BLP</i>) with continuous variables. First, a brief summar...

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>,...

Quel octogone de diamère unité (ou petit octogone) possède la plus grande surface ou le plus grand périmètre? Serait-ce l'octogone régulier? Eh! non, il n'en...

This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitatio...

An alternative definition of the linear bilevel programming problem <i>BLP</i> has recently been proposed by Lu, Shi, and Zhang. This note shows that the pr...

A previous analysis of second-order behavior of pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more gen...

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...