x, y \in C \implies t x + (1-t) y \in C, \quad \text{for all $t \in [0,1]$}. joining $x$ and $y$ lies entirely in $C$. See Figure \ref{fig:convex_set}. A \emph{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 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) ...

Abstract: This chapter helps the students to identify convex functions, convex sets, and convex optimization problems. It presents comparison between a convex and a non‐convex function. The chapter ...

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

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 ...

American Journal of Mathematics, Vol. 138, No. 2 (April 2016), pp. 499-527 (29 pages) This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded ...

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

To solve the problem on inaccuracy when estimating the point spread function (PSF) of the ideal original image in traditional projection onto convex set (POCS) super-resolution (SR) reconstruction, ...

ABSTRACT: By applying the q-derivative, we introduce two new subclasses of p-valent functions with positive coefficients. By means of the well-known Jack’s lemma, some inequalities related to starlike ...