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Mesh Adaptive Direct Search Algorithms for Constrained Optimization
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
Analysis of Generalized Pattern Searches
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
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Expand
Pooling Problem: Alternate Formulations and Solution Methods
- Charles Audet, J. Brimberg, P. Hansen, S. Digabel, Nenad Mladenovic
- Computer Science, Mathematics
- Manag. Sci.
- 1 May 2000
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
Pattern Search Algorithms for Mixed Variable Programming
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
A branch and cut algorithm for nonconvex quadratically constrained quadratic programming
- Charles Audet, P. Hansen, B. Jaumard, G. Savard
- Mathematics, Computer Science
- Math. Program.
- 1 December 1997
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
Multiobjective Optimization Through a Series of Single-Objective Formulations
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
OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions
- Mark A. Abramson, Charles Audet, J. Dennis, S. Digabel
- Mathematics, Computer Science
- SIAM J. Optim.
- 1 February 2008
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
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 bound… Expand
Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points
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