Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems

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Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems (2004)

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by Mark A. Abramson , Charles Audet , J.E. Dennis Jr.

Venue:	SIAM Journal on Optimization
Citations:	55 - 6 self

BibTeX

@ARTICLE{Abramson04filterpattern,
    author = {Mark A. Abramson and Charles Audet and J.E. Dennis Jr.},
    title = {Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems},
    journal = {SIAM Journal on Optimization},
    year = {2004},
    volume = {11},
    pages = {573--594}
}

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Abstract

A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the Audet-Dennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPS-filter algorithms for general nonlinear constraints. In generalizing existing algorithms, new theoretical convergence results are presented that reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are required to apply the algorithm, a hierarchy of theoretical convergence results based on the Clarke calculus is given, in which local smoothness dictate what can be proved about certain limit points generated by the algorithm. To demonstrate the usefulness of the algorithm, the algorithm is applied to the design of a loadbearing thermal insulation system. We believe this is the first algorithm with provable convergence results to directly target this class of problems.

Keyphrases

filter pattern search algorithm mixed variable constrained optimization problem mixed variable optimization problem mixed variable optimization clarke calculus certain limit point class combine new class smoothness assumption gps-filter algorithm loadbearing thermal insulation system specific class first algorithm local smoothness provable convergence result theoretical convergence result general nonlinear constraint new theoretical convergence result local continuity audet-dennis generalized pattern search

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