A Pattern Search Filter Method for Nonlinear Programming Without Derivatives

Abstract

This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that either improves the objective function value or the value of some function that measures the constraint violation. The new algorithm does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. A key feature of the new algorithm is that it preserves the useful division into global SEARCH and local POLL steps. It is shown here that the algorithm identifies limit points at which optimality conditions depend on local smoothness of the functions. Stronger optimality conditions are guaranteed for smoother functions. In the absence of general constraints, the proposed algorithm and its convergence analysis generalize the previous work on unconstrained, bound constrained and linearly constrained generalized pattern search. The algorithm is illustrated on some test examples and on an industrial wing planform engineering design application.

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Document Details

Document Type
Technical Report
Publication Date
Jun 12, 2003
Accession Number
ADA445706

Entities

People

  • Charles Audet
  • J. E. Dennis Jr.

Organizations

  • Polytechnic School of Montreal

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Computer Programming
  • Computers
  • Engineering
  • Equations
  • Evolutionary Algorithms
  • Geometry
  • Mathematical Programming
  • Mathematics
  • Nonlinear Programming
  • Numbers
  • Operations Research
  • Optimization
  • Paper
  • Planform

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.