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Mesh Adaptive Direct Search Algorithms for Constrained Optimization
tl;dr
We introduce the mesh adaptive direct search (MADS) class of algorithms which extends the generalized pattern search (GPS) class by allowing local exploration, called polling, in an asymptotically dense set of directions in the space of optimization variables. Expand
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Analysis of Generalized Pattern Searches
tl;dr
We show that the strength of the optimality conditions at a limit point depends not only on the algorithm, but also on the directions it uses and on the smoothness of the objective at the limit point. Expand
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A Pattern Search Filter Method for Nonlinear Programming without Derivatives
tl;dr
This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Expand
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Pooling Problem: Alternate Formulations and Solution Methods
tl;dr
The pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. Expand
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Pattern Search Algorithms for Mixed Variable Programming
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We present a class of direct search algorithms to provide limit points that satisfy some appropriate necessary conditions for local optimality for such problems. Expand
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A branch and cut algorithm for nonconvex quadratically constrained quadratic programming
tl;dr
We present a branch and cut algorithm that yields in finite time, a globally ε-optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. Expand
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Multiobjective Optimization Through a Series of Single-Objective Formulations
tl;dr
This work deals with bound constrained multiobjective optimization (MOP) of nonsmooth functions for problems where the structure of the objective functions either cannot be exploited, or are absent. Expand
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OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions
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The purpose of this paper is to introduce a new way of choosing directions for the mesh adaptive direct search (Mads) class of algorithms that uses an orthogonal positive spanning set of polling directions. Expand
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Pattern search algorithms for mixed variable general constrained optimization problems
Abstract : A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented The Audet-Dennis Generalized Pattern Search (GPS) algorithm for boundExpand
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Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points
tl;dr
A previous analysis of second-order behavior of generalized pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search (MADS) algorithms. Expand
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