Unified nonlinear Lagrangian approach to duality and optimal paths

C. Y. Wang; Xiaoqi Yang; X. M. Yang

doi:10.1007/s10957-007-9225-x

Unified nonlinear Lagrangian approach to duality and optimal paths

C. Y. Wang, Xiaoqi Yang, X. M. Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	85-100
Number of pages	16
Journal	Journal of Optimization Theory and Applications
Volume	135
Issue number	1
DOIs	https://doi.org/10.1007/s10957-007-9225-x
Publication status	Published - 1 Oct 2007

Keywords

Finite termination
Nonlinear augmented Lagrangians
Nonlinear Lagrangians
Optimal paths
Zero duality gap

ASJC Scopus subject areas

Applied Mathematics
Control and Optimization
Management Science and Operations Research

More information

10.1007/s10957-007-9225-x

Cite this

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AB - 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.

KW - Finite termination

KW - Nonlinear augmented Lagrangians

KW - Nonlinear Lagrangians

KW - Optimal paths

KW - Zero duality gap

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Unified nonlinear Lagrangian approach to duality and optimal paths

Abstract

Keywords

ASJC Scopus subject areas

More information

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