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

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

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 ...

Let $S$ denote the functions that are analytic and univalent in the open unit disk and satisfy $f(0) = 0$ and $f\prime(0) = 1$. Also, let $K, St, S_R$, and $C$ be the ...