Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
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
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
Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point
SIAM Journal on Optimization
Pattern Search Algorithms for Bound Constrained Minimization
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
Frames and Grids in Unconstrained and Linearly Constrained Optimization: A Nonsmooth Approach
SIAM Journal on Optimization
Convex Optimization
Mathematical Programming: Series A and B
Implementing Generating Set Search Methods for Linearly Constrained Minimization
SIAM Journal on Scientific Computing
Pattern search in the presence of degenerate linear constraints
Optimization Methods & Software
International Journal of Applied Mathematics and Computer Science - SPECIAL SECTION: Efficient Resource Management for Grid-Enabled Applications
Engineering Applications of Artificial Intelligence
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We propose a Generalized Pattern Search (GPS) method to solve a class of nonsmooth minimization problems, where the set of nondifferentiability is included in the union of known hyperplanes and, therefore, is highly structured. Both unconstrained and linearly constrained problems are considered. At each iteration the set of poll directions is enforced to conform to the geometry of both the nondifferentiability set and the boundary of the feasible region, near the current iterate. This is the key issue to guarantee the convergence of certain subsequences of iterates to points which satisfy first-order optimality conditions. Numerical experiments on some classical problems validate the method.