Duality and Exact Penalization for Vector Optimization via Augmented Lagrangian |
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| Authors: | X X Huang and X Q Yang |
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| Institution: | (1) Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China;(2) Present address: Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong;(3) Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong |
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| 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. |
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| Keywords: | Vector optimization augmented Lagrangian duality exact penalization nonlinear Lagrangian |
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