Unified Nonlinear Lagrangian Approach to Duality and Optimal Paths |
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| Authors: | C Y Wang X Q Yang X M Yang |
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| Institution: | (1) Institute of Operations Research, Qufu Normal University, Qufu, China;(2) Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China;(3) Department of Mathematics, Chongqing Normal University, Chongqing, China |
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| Abstract: | In the context of an inequality constrained optimization problem, we present a unified nonlinear Lagrangian dual scheme and
establish necessary and sufficient conditions for the zero duality gap property. From these results, we derive necessary and
sufficient conditions for four classes of zero duality gap properties and establish the equivalence among them. Finally, we
obtain the convergence of an optimal path for the unified scheme and present a sufficient condition for the finite termination
of the optimal path.
This research was partially supported by the Research Grants Council of Hong Kong Grant PolyU 5250/03E, the National Natural
Science Foundation of China Grants 10471159 and 10571106, NCET, and the Natural Science Foundation of Chongqing |
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| Keywords: | Nonlinear Lagrangians Nonlinear augmented Lagrangians Zero duality gap Optimal paths Finite termination |
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