Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints

  • Authors:

  • Jean-Baptiste Hiriart-Urruty

  • Affiliations:

  • Laboratoire MIP, UMR 5640, U.F.R. Mathématiques, Informatique, Gestion, Université Paul Sabatier, 118 Route de Narbonne, 31062 Topulouse Cedex 4, France (E-mail: jbhu@cict.fr

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2001

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Abstract

For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of ε-subdifferentials of convex functions and ε-normal directions, to convex sets. By specializing the problem of maximizing a convex function over a convex set, we find explicit conditions for optimality.