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

  • Authors:

  • David Yang Gao

  • Affiliations:

  • Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA.

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2000

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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 \realn can be reformulated into certain smooth/convex unconstrained dual problems in \realm with m≤slant 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.