A Multivariate Global Optimization Using Linear Bounding Functions

  • Authors:

  • Xiaojun Wang;Tsu-Shuan Chang

  • Affiliations:

  • Applied Mathematics Group, Department of Mathematics, University of California, Davis, CA 95616, USA/;Department of Electrical and Computer Engineering, University of California, Davis, CA 95616, USA

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

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Abstract

Recently linear bounding functions (LBFs) were proposed and used to findϵ-global minima. This paper presents an LBF-basedalgorithm for multivariate global optimization problems. The algorithmconsists of three phases. In the global phase, big subregions notcontaining a solution are quickly eliminated and those which possiblycontain the solution are detected. An efficient scheme for the local phaseis developed using our previous local minimization algorithm, which isglobally convergent with superlinear/quadratic rate and does not requireevaluation of gradients and Hessian matrices. To ensure that the foundminimizers are indeed the global solutions or save computation effort, athird phase called the verification phase is often needed. Under adequateconditions the algorithm finds the ϵ-global solution(s)within finite steps. Numerical testing results illustrate how the algorithmworks, and demonstrate its potential and feasibility.