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 ...

Abstract: The recently developed approach to motion planning in Graphs of Convex Sets (GCS) provides an efficient framework for computing shortest-distance collision-free paths using convex ...

Abstract: The recently developed approach to motion planning in graphs of convex sets (GCS) provides an efficient framework for computing shortest-distance collision-free paths using convex ...

Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.

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 ...

ABSTRACT: In this paper, we present some properties of m-convex stochastic processes. The most important results are: a generalization of the sandwich theorem and a result on Hyers-Ulam stability, ...