Pattern Search Methods for Linearly Constrained Minimization in the Presence of Degeneracy

Abstract

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 constrains, and this is used to define the POLL set for that iteration. The contribution of this paper is to provide a detailed algorithm for constructing the set of directions at a current iterate whether or not the constraints are degenerate. The main difficulty in the degenerate case is in classifying constraints as redundant and nonredundant . We give a short survey of the main definitions and methods concerning redundancy and propose an approach, which may be useful for other active set algorithms, to identify the nonredundant constraints.

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Document Details

Document Type
Technical Report
Publication Date
Aug 10, 2003
Accession Number
ADA451780

Entities

People

  • J. E. Dennis Jr.
  • Olga A. Brezhneva

Organizations

  • University of Minnesota

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Classification
  • Computer Programming
  • Convergence
  • Decomposition
  • Generators
  • Geometry
  • Identification
  • Inequalities
  • Mathematical Programming
  • Mathematics
  • Numbers
  • Optimization
  • Theorems

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  • Operations Research
  • Theoretical Analysis.

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  • Space