Abstract
In this paper, we present a unified approach for studying convex composite multiobjective optimization problems via asymptotic analysis. We characterize the nonemptiness and compactness of the weak Pareto optimal solution sets for a convex composite multiobjective optimization problem. Then, we employ the obtained results to propose a class of proximal-type methods for solving the convex composite multiobjective optimization problem, and carry out their convergence analysis under some mild conditions.
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Acknowledgments
The author thanks two anonymous referees for carefully reading the original submission and supplying many helpful suggestions, which greatly improved the paper. The author thanks Prof. X. Q. Yang, The Hong Kong Polytechnic University, for his teaching. The author also thanks Prof. J. Chen, Tsinghua University, for his some useful suggestions in the revised versions. This work is supported by the National Science Foundation of China (11001289) and the Key Project of Chinese Ministry of Education (211151), the National Science Foundation of Chongqing Science and Technology Commission (CSTC, 2011BB0118) and Research Grant of Education Committee of Chongqing (KJ110633).
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Chen, Z. Asymptotic analysis in convex composite multiobjective optimization problems. J Glob Optim 55, 507–520 (2013). https://doi.org/10.1007/s10898-012-0032-z
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DOI: https://doi.org/10.1007/s10898-012-0032-z
Keywords
- Convex composite multiobjective optimization
- Asymptotic analysis
- Proximal-type method
- Nonemptiness and compactness
- Weak Pareto optimal solution