Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

Matrix inequalities and convex functions constitute a central theme in modern mathematical analysis, with far‐reaching implications across numerical analysis, optimisation, quantum information, and ...

Transactions of the American Mathematical Society, Vol. 327, No. 2 (Oct., 1991), pp. 795-813 (19 pages) Let Γ(X) denote the proper, lower semicontinuous, convex functions on a Banach space X, equipped ...

This course discusses basic convex analysis (convex sets, functions, and optimization problems), optimization theory (linear, quadratic, semidefinite, and geometric programming; optimality conditions ...

The study of inequalities and integral operators in convex analysis has evolved into a rich field that unites classical methods with modern extensions. At its core, convex analysis examines functions ...