Canonical duality for solving general nonconvex constrained problems

Canonical duality for solving general nonconvex constrained problems

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Article ID: iaor20163736
Volume: 10
Issue: 8
Start Page Number: 1763
End Page Number: 1779
Publication Date: Dec 2016
Journal: Optimization Letters
Authors: ,
Keywords: heuristics, programming: nonlinear
Abstract:

This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided.While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints. Some fundamental concepts such as the objectivity and Lagrangian in nonlinear programming are addressed.

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