New calculus rules of relative subdifferentials and applications to constrained optimization problems

Cao Thanh Tinh, Xiaolong Qin (), Thai Doan Chuong and Vo Duc Thinh
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Cao Thanh Tinh: Vietnam National University
Xiaolong Qin: Hangzhou Normal University, Department of Mathematics
Thai Doan Chuong: Brunel University of London, Department of Mathematics
Vo Duc Thinh: Dong Thap University, School of Education

Journal of Global Optimization, 2025, vol. 93, issue 3, No 10, 897-922

Abstract: Abstract This paper investigates properties and calculus rules, including new calculation formulas of chain rules and maximum-pointwise rules for the relative subdifferentials of nondifferentiable functions. Based on these properties and calculation rules, we establish novel optimality conditions without normal cones for a class of optimization problems with set constraints. These results include, among other different properties, Fritz-John and Karush-Kuhn-Tucker necessary conditions for optimization problems involving equality, inequality and set constraints. We demonstrate through illustrative examples that the obtained optimality conditions are not only sharper than the existing ones even when restricted them in a finite-dimensional setting, but also applicable under weaker qualification assumptions.

Keywords: Constraint qualification; Chain rule; Maximum-pointwise function; Optimality condition; Relative subdifferential; 49J53; 90C30; 90C31 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01551-z

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