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 that question with respect to Generalized Pattern Search (GPS) ...

A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the Audet-Dennis Generalized Pattern Search (GPS) algorithms for bound ...

Recently, general definitions of pattern search methods for both unconstrained and linearly constrained optimization were presented. It was shown under mild conditions, that there exists a subsequence of iterates converging ...

This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that either improves the objective function ...

We pursue the study of concavity cuts for the disjoint bilinear programming problem. This optimization problem has two equivalent symmetric linear maxmin reformulations, leading to two sets of concavity cuts. We first ...

Many engineering optimization problems involve a special kind of discrete variable that can be represented by a number, but this representation has no significance. Such variables arise when a decision involves some situation ...

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

We present a branch and cut algorithm that yields in finite time, a globally epsilon-optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. ...

In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that ...

This paper introduces the Mesh Adaptive Direct Search (MADS) class of algorithms for nonlinear optimization. MADS extends the Generalized Pattern Search (GPS) class by allowing local exploration, called polling, in a dense ...