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Mesh Adaptive Direct Search Algorithms for Constrained Optimization
TLDR
The main result of this paper is that the general MADS framework is flexible enough to allow the generation of an asymptotically dense set of refining directions along which the Clarke derivatives are nonnegative.
Analysis of Generalized Pattern Searches
TLDR
A simple convergence analysis is provided that supplies detail about the relation of optimality conditions to objective smoothness properties and to the defining directions for the algorithm, and it gives previous results as corollaries.
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
TLDR
This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance that preserves the division into SEARCH and local POLL steps, which allows the explicit use of inexpensive surrogates or random search heuristics in the SEARCH step.
Pattern Search Algorithms for Mixed Variable Programming
TLDR
This work presents a class of direct search algorithms to provide limit points that satisfy some appropriate necessary conditions for local optimality for such problems and gives a more expensive version of the algorithm that guarantees additional necessary optimality conditions.
Multiobjective Optimization Through a Series of Single-Objective Formulations
TLDR
A new algorithm is proposed called BOP, called for the biobjective optimization (BOP) problem, which generates an approximation of the Pareto front by solving a series of single-objective formulations of BOP.
Pooling Problem: Alternate Formulations and Solution Methods
TLDR
This paper investigates how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem and considers two standard models: One is based primarily on flow variables, and the other relies on the proportion of flows entering pools.
Derivative-Free and Blackbox Optimization
TLDR
DFO algorithms have principally fallen into one of two categories: direct search methods and modelbased methods, and researchers began mixing direct search and model-based methods to create hybrid methods with improved performance.
A branch and cut algorithm for nonconvex quadratically constrained quadratic programming
TLDR
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.
OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions
TLDR
A new way of choosing directions for the mesh adaptive direct search (Mads) class of algorithms, where the polling directions are chosen deterministically, ensuring that the results of a given run are repeatable, and that they are orthogonal to each other, which yields convex cones of missed directions at each iteration.
Pattern search algorithms for mixed variable general constrained optimization problems
TLDR
A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented that can exploit any available derivative information to speed convergence without sacrificing the flexibility often employed by GPS methods to find better local optima.
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