Duality and Exact Penalization for Vector Optimization via Augmented Lagrangian

X. X. Huang and X. Q. Yang
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X. X. Huang: Chongqing Normal University
X. Q. Yang: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2001, vol. 111, issue 3, No 7, 615-640

Abstract: Abstract In this paper, we introduce an augmented Lagrangian function for a multiobjective optimization problem with an extended vector-valued function. On the basis of this augmented Lagrangian, set-valued dual maps and dual optimization problems are constructed. Weak and strong duality results are obtained. Necessary and sufficient conditions for uniformly exact penalization and exact penalization are established. Finally, comparisons of saddle-point properties are made between a class of augmented Lagrangian functions and nonlinear Lagrangian functions for a constrained multiobjective optimization problem.

Keywords: Vector optimization; augmented Lagrangian; duality; exact penalization; nonlinear Lagrangian (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/A:1012654128753

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