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First- and second-order optimality conditions of nonsmooth sparsity multiobjective optimization via variational analysis

Author

Listed:
  • Jiawei Chen

    (Southwest University)

  • Huasheng Su

    (Southwest University)

  • Xiaoqing Ou

    (Chongqing College of Humanities, Science & Technology)

  • Yibing Lv

    (Yangtze University)

Abstract

In this paper, we investigate optimality conditions of nonsmooth sparsity multiobjective optimization problem (shortly, SMOP) by the advanced variational analysis. We present the variational analysis characterizations, such as tangent cones, normal cones, dual cones and second-order tangent set, of the sparse set, and give the relationships among the sparse set and its tangent cones and second-order tangent set. The first-order necessary conditions for local weakly Pareto efficient solution of SMOP are established under some suitable conditions. We also obtain the equivalence between basic feasible point and stationary point defined by the Fréchet normal cone of SMOP. The sufficient optimality conditions of SMOP are derived under the pseudoconvexity. Moreover, the second-order necessary and sufficient optimality conditions of SMOP are established by the Dini directional derivatives of the objective function and the Bouligand tangent cone and second-order tangent set of the sparse set.

Suggested Citation

  • Jiawei Chen & Huasheng Su & Xiaoqing Ou & Yibing Lv, 2024. "First- and second-order optimality conditions of nonsmooth sparsity multiobjective optimization via variational analysis," Journal of Global Optimization, Springer, vol. 89(2), pages 303-325, June.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:2:d:10.1007_s10898-023-01357-x
    DOI: 10.1007/s10898-023-01357-x
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    1. Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.
    2. Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
    3. Jiawei Chen & Yu-Hong Dai, 2023. "Multiobjective optimization with least constraint violation: optimality conditions and exact penalization," Journal of Global Optimization, Springer, vol. 87(2), pages 807-830, November.
    4. D. Aussel, 1998. "Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 29-45, April.
    5. Amir Beck & Yakov Vaisbourd, 2016. "The Sparse Principal Component Analysis Problem: Optimality Conditions and Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 119-143, July.
    6. Jianjun Gao & Duan Li, 2013. "Optimal Cardinality Constrained Portfolio Selection," Operations Research, INFORMS, vol. 61(3), pages 745-761, June.
    7. Jiawei Chen & La Huang & Shengjie Li, 2018. "Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 794-823, September.
    8. Qamrul Hasan Ansari & Elisabeth Köbis & Pradeep Kumar Sharma, 2019. "Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 817-839, June.
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