Hit-and run algorithms for the identification of nonredundant linear inequalities
Mathematical Programming: Series A and B
Integer and combinatorial optimization
Integer and combinatorial optimization
Journal of Optimization Theory and Applications
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Constraint classification in mathematical programming
Mathematical Programming: Series A and B
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
Double Description Method Revisited
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
Frames and Grids in Unconstrained and Linearly Constrained Optimization: A Nonsmooth Approach
SIAM Journal on Optimization
Second-Order Behavior of Pattern Search
SIAM Journal on Optimization
Generalized Pattern Search methods for a class of nonsmooth optimization problems with structure
Journal of Computational and Applied Mathematics
PSwarm: a hybrid solver for linearly constrained global derivative-free optimization
Optimization Methods & Software - GLOBAL OPTIMIZATION
Hi-index | 0.00 |
This paper deals with generalized pattern search (GPS) algorithms for linearly constrained optimization. At each iteration, the GPS algorithm generates a set of directions that conforms to the geometry of any nearby linear constraints. This set is then used to construct trial points to be evaluated during the iteration. In a previous work, Lewis and Torczon developed a scheme for computing the conforming directions, however, the issue of degeneracy merits further investigation. The contribution of this paper is to provide a detailed algorithm for constructing the set of directions whether or not the constraints are degenerate. One difficulty in the degenerate case is the classification of constraints as redundant or nonredundant. We give a short survey of the main definitions and methods for treating redundancy and propose an approach to identify nonredundant ε-active constraints. We also introduce a new approach for handling nonredundant linearly dependent constraints, which maintains GPS convergence properties without significantly increasing computational cost. Some simple numerical tests illustrate the effectiveness of the algorithm.