A Proximal-Type Method for Convex Vector Optimization Problem in Banach Spaces |
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Authors: | Zhe Chen Kequan Zhao |
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Institution: | 1. Department of Mathematics and Computer Science , Chongqing Normal University , Chongqing, China;2. Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom Kowloon, Hong Kong zhe505@yahoo.com.cn;4. Department of Mathematics and Computer Science , Chongqing Normal University , Chongqing, China |
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Abstract: | In this paper, we consider a convex vector optimization problem of finding weak Pareto optimal solutions from a uniformly convex and uniformly smooth Banach space to a real Banach space, with respect to the partial order induced by a closed, convex, and pointed cone with a nonempty interior. We introduce a vector-valued proximal-type method based on the Lyapunov functional, carry out convergent analysis on this method, and prove that any sequence generated by the method weakly converges to a weak Pareto optimal solution of the vector optimization problem under some mild conditions. Our results improve and generalize some known results. |
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Keywords: | Banach spaces Lyapunov functional Proximal-type method Vector optimization Weakly converge Weak Pareto optimal solution |
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