Optimality Conditions and Lagrange Dualities for Optimization Problems Involving $$\varPhi _c$$ Φ c -convex Functions

Ling-Li Hu () and Dong-Hui Fang ()
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Ling-Li Hu: Sun Yat-sen University
Dong-Hui Fang: Jishou University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 5, 18 pages

Abstract: Abstract In this paper, we consider an optimization problem in which the objective is the difference of two $$\varPhi _c$$ Φ c -convex functions and the constraints include a set constraint and a cone constraint. We first introduce three new constraint qualifications regarding the c-subdifferential and the epigraph properties of the involved functions. Under the new constraint qualifications, we provide some sufficient conditions for optimality conditions to hold. Similarly, strong and total Lagrange dualities for the optimization problem involving the difference of two $$\varPhi _c$$ Φ c -convex functions are also given.

Keywords: Optimality condition; Strong duality; Total duality; $$\varPhi _c$$ Φ c -convex function; 90C26; 90C46 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02755-9

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