We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
First- and second-order optimality conditions of nonsmooth sparsity multiobjective optimization via variational analysis.
- Authors
Chen, Jiawei; Su, Huasheng; Ou, Xiaoqing; Lv, Yibing
- 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.
- Subjects
DERIVATIVES (Mathematics); DIRECTIONAL derivatives; NONSMOOTH optimization; TANGENT function; CONES
- Publication
Journal of Global Optimization, 2024, Vol 89, Issue 2, p303
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-023-01357-x