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Journal of Global Optimization

, Volume 17, Issue 1–4, pp 127–160 | Cite as

Canonical Dual Transformation Method and Generalized Triality Theory in Nonsmooth Global Optimization*

  • David Yang Gao
Article

Abstract

This paper presents, within a unified framework, a potentially powerful canonical dual transformation method and associated generalized duality theory in nonsmooth global optimization. It is shown that by the use of this method, many nonsmooth/nonconvex constrained primal problems in ℝ n can be reformulated into certain smooth/convex unconstrained dual problems in ℝ m with m ⩽ n and without duality gap, and some NP-hard concave minimization problems can be transformed into unconstrained convex minimization dual problems. The extended Lagrange duality principles proposed recently in finite deformation theory are generalized suitable for solving a large class of nonconvex and nonsmooth problems. The very interesting generalized triality theory can be used to establish nice theoretical results and to develop efficient alternative algorithms for robust computations.

Bi-duality Canonical dual transformation D.C. optimization Duality Global optimization Nonconvexity Nonsmoothness Reformulation Triality 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • David Yang Gao
    • 1
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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