A Probability-One Homotopy Algorithm for Nonsmooth Equations and Mixed Complementarity Problems

Abstract

A probability-one homotopy algorithm for solving nonsmooth equations is described. This algorithm is able to solve problems involving highly nonlinear equations, where the norm of the residual has non-global local minima. The algorithm is based on constructing homotopy mappings mentarity problems through the use of MCP functions and associated smoothers. This specialized algorithm includes an option to ensure that all iterates remain feasible. Easily satisfiable sufficient conditions are given to ensure that the homotopy zero curve remains feasible, and global convergence properties for the MCP algorithm are developed. Computational results on the MCPLIB test library demonstrate the effectiveness of the algorithm.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADA445723

Entities

People

  • Layne T. Watson
  • Stephen C. Billups

Organizations

  • University of Colorado Boulder

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Computer Science
  • Convergence
  • Differential Equations
  • Equations
  • Iterations
  • Linear Algebra
  • Mathematics
  • Notation
  • Numbers
  • Partial Differential Equations
  • Probability
  • Real Numbers
  • Residuals
  • Sequences
  • Standards

Fields of Study

  • Mathematics

Readers

  • Operations Research