Journal of Global Optimization

, Volume 7, Issue 4, pp 337–363

αBB: A global optimization method for general constrained nonconvex problems

  • I. P. Androulakis
  • C. D. Maranas
  • C. A. Floudas
Article

DOI: 10.1007/BF01099647

Cite this article as:
Androulakis, I.P., Maranas, C.D. & Floudas, C.A. J Glob Optim (1995) 7: 337. doi:10.1007/BF01099647

Abstract

A branch and bound global optimization method,αBB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convex relaxation of the original nonconvex problem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the α parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finiteε-convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method,αBB, is implemented in C and tested on a variety of example problems.

Keywords

Global optimizationconstrained optimizationconvex relaxation

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • I. P. Androulakis
    • 1
  • C. D. Maranas
    • 1
  • C. A. Floudas
    • 1
  1. 1.Department of Chemical EngineeringPrinceton UniversityPrinceton