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

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.

Brief Overview A large body of problems in information theory, estimation theory, finance and machine learning can be formulated as max P X∈F G(P X) (∗) max P X ∈ F G (P X) (∗) where G(⋅) G () is some ...

The main result proved in this paper is that the ratio of the square of a nonnegative convex function to a strictly positive concave function is convex over a convex domain. Some particular cases of ...

In this paper we are concerned with the problem of finding the global minimum of a concave function over a closed, convex, possibly unbounded set in R n. The intrinsic difficulty of this problem is ...