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

Jiawei Chen (), Huasheng Su (), Xiaoqing Ou () and Yibing Lv ()
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Jiawei Chen: Southwest University
Huasheng Su: Southwest University
Xiaoqing Ou: Chongqing College of Humanities, Science & Technology
Yibing Lv: Yangtze University

Journal of Global Optimization, 2024, vol. 89, issue 2, No 3, 303-325

Abstract: 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.

Keywords: Nonsmooth multiobjective optimization; Sparsity; Optimality conditions; Second-order tangent set; Variational analysis (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01357-x

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