Computational Experience with a New Class of Convex Underestimators: Box-constrained NLP Problems

  • Authors:

  • Ioannis G. Akrotirianakis;Christodoulos A. Floudas

  • Affiliations:

  • Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA e-mail: floudas@titan.princeton.edu;Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA e-mail: floudas@titan.princeton.edu

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2004

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Abstract

In Akrotirianakis and Floudas (2004) we presented the theoretical foundations of a new class of convex underestimators for C2 nonconvex functions. In this paper, we present computational experience with those underestimators incorporated within a Branch-and-Bound algorithm for box-conatrained problems. The algorithm can be used to solve global optimization problems that involve C2 functions. We discuss several ways of incorporating the convex underestimators within a Branch-and-Bound framework. The resulting Branch-and-Bound algorithm is then used to solve a number of difficult box-constrained global optimization problems. A hybrid algorithm is also introduced, which incorporates a stochastic algorithm, the Random-Linkage method, for the solution of the nonconvex underestimating subproblems, arising within a Branch-and-Bound framework. The resulting algorithm also solves efficiently the same set of test problems.