Convergent Outer Approximation Algorithms for Solving Unary Programs

  • Authors:

  • Reiner Horst;Ulrich Raber

  • Affiliations:

  • Department of Mathematics, University of Trier, D-54286 Trier, Germany;Department of Mathematics, University of Trier, D-54286 Trier, Germany

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 1998

Quantified Score

Hi-index 0.01

Visualization

Abstract

Interesting cutting plane approaches for solving certain difficultmultiextremal global optimization problems can fail to converge. Examplesinclude the concavity cut method for concave minimization and Ramana‘srecent outer approximation method for unary programs which are linearprogramming problems with an additional constraint requiring that an affinemapping becomes unary. For the latter problem class, new convergent outerapproximation algorithms are proposed which are based on sufficiently deepl_∞-norm or quadratic cuts.Implementable versions construct optimal simplicial inner approximations ofEuclidean balls and of intersections of Euclidean balls with halfspaces,which are of general interest in computational convexity. Computationalbehavior of the algorithms depends crucially on the matrices involved in theunary condition. Potential applications to the global minimization ofindefinite quadratic functions subject to indefinite quadratic constraintsare shown to be practical only for very small problem sizes.