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math.OC2025
First-Order Characterizations of Strong Quasiconvexity and a Quasimonotonicity Gap
Nguyen Xuan Duy Bao, Nguyen Mau Nam
We study first-order conditions for Gâteaux differentiable strongly quasiconvex functions on open convex subsets of normed spaces. First, we prove that the value-order gradient con…
math.OC2025
Qualitative and Generalized Differentiation Properties of Optimal Value Functions with Applications to Duality
V. S. T. Long, B. S. Mordukhovich, N. M. Nam +1
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nea…