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

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 ...

Convex optimisation constitutes a fundamental area in applied mathematics where the objective is to identify the minimum of a convex function subject to a set of convex constraints. This framework ...

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 ...

Transactions of the American Mathematical Society, Vol. 192 (May, 1974), pp. 285-292 (8 pages) The closed convex hull and extreme points are obtained for the functions which are convex, starlike, and ...

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 ...

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, ...

Show that the set is convex if and only if its intersection with any line is convex. Show that the convex hull of the $S$ set is the intersection of all convex sets ...