On generalized Fenchel-Moreau theorem and second-order characterization for convex vector functions
Phan Nhật Tĩnh, Do Sang Kim · Fixed Point Theory and Applications · 2013
Based on the concept of conjugate and biconjugate maps introduced in (Tan and Tinh in Acta Math. Viet. 25:315-345, 2000) we establish a full generalization of the Fenchel-Moreau theorem for the vector case. Besides this, by using the Clarke generalized first-order derivative for locally Lipschitz vector functions, we establish a first-order characterization for monotone operators. Consequently, a second-order characterization for convex vector functions is obtained. MSC: 26B25, 49J52, 49J99, 90C46, 90C29.