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...

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...