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Convexity and Monotonicity in Global Optimization

  • Hoang Tuy
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 54)

Abstract

Convexity and monotonicity are two properties of crucial importance in the deterministic approaches to global optimization. An overwhelming majority of deterministic global optimization methods developed over the last three decades are based on exploiting convexity in some form or another. On the other hand, a recently initiated theory of monotonic optimization is based on exploiting monotonicity solely. By drawing a parallel between the two approaches: d.c. (difference-convex) optimization and d.m. (difference-monotonic) optimization, this paper focuses on aspects which make the d.m. approach particularly attractive from a numerical point of view, at least in some important cases of interest. An improved form of an earlier developed basic algorithm for d.m. optimization is presented and applied to polynomial programming to illustrate the wide applicability of the new approach.

Keywords

Difference of convex (d.c.) functions Difference of monotonic (d.m.) functions Normal sets Canonical monotonic optimization problem Polyblock algorithm Polynomial programming 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Hoang Tuy
    • 1
  1. 1.Institute of MathematicsBo Ho, HanoiVietnam

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