Wenqing Wang, Yihong Xu, Qamrul Hasan Ansari, Nonlinear characterizations for set optimization with a variable structure and applications
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DOI: 10.23952/jnva.10.2026.6.05
Volume 10, Issue 6, 1 December 2026, Pages 1117-1144
Abstract. In this paper, we obtain some properties of a generalized Gerstewitz’s function with respect to a variable structure. Then, by using the scalarization function and the image space analysis, necessary and sufficient optimality conditions for the solutions are established. In addition, we propose two nonlinear weak separation functions for the set optimization problems and introduce a generalized Lagrangian set-valued mapping to obtain the relationship between the saddle points and the existence of a nonlinear separation. Finally, as applications of the main results of this paper, we examine traffic network problems with interval-valued cost functions and medical image registration.
How to Cite this Article:
W. Wang, Y. Xu, Q.H. Ansari, Nonlinear characterizations for set optimization with a variable structure and applications, J. Nonlinear Var. Anal. 10 (2026), 1117-1144.