Combined bound-grid-factor constraints for enhancing RLT relaxations for polynomial programs

  • Authors:

  • Hanif D. Sherali;Evrim Dalkiran

  • Affiliations:

  • Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061;Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2011

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Abstract

This paper studies the global optimization of polynomial programming problems using Reformulation-Linearization Technique (RLT)-based linear programming (LP) relaxations. We introduce a new class of bound-grid-factor constraints that can be judiciously used to augment the basic RLT relaxations in order to improve the quality of lower bounds and enhance the performance of global branch-and-bound algorithms. Certain theoretical properties are established that shed light on the effect of these valid inequalities in driving the discrepancies between RLT variables and their associated nonlinear products to zero. To preserve computational expediency while promoting efficiency, we propose certain concurrent and sequential cut generation routines and various grid-factor selection rules. The results indicate a significant tightening of lower bounds, which yields an overall reduction in computational effort for solving a test-bed of polynomial programming problems to global optimality in comparison with the basic RLT procedure as well as the commercial software BARON.