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 ...

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 ...

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) ...

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 ...

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

Abstract. In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of ...

Convex geometry and combinatorial optimisation form a vibrant nexus of research that bridges theoretical mathematics with practical algorithm design. The study of convex sets and their structural ...

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 ...

1 Russian-Armenian (Slavonic) University, Yerevan, Armenia. 2 Institute of Mathematics Armenian Academy of Sciences, Yerevan, Armenia. The problem of reconstruction of a convex body from the mean and ...