This post deals with the minimization of the log barrier function that is: where defined as We shall attempt an intuitive explanation on the solution of the following unconstrained minimization problem First off, let’s say our set of inequalities defined by is closed, the […]

# Convex Optimization

The following lecture talks about the Markowitz Portfolio Optimization problem in convex optimization. Indeed, many variants of this problem exists, but the classical one looks like this where is an sized vector containing the amount of assets to invest in. The vector is the mean of the relative […]

In this lecture, we talk about equivalent reformulations, that are reformulations done on the initial problem of the form (1) A very interesting question is the following. Assume we got two problems and that are equivalent problems. Are their duals, (hereby denoted by and , respectively) the same ? […]

In a previous post of mine, I talked about CVXOPT Programming. In this one, we’ll introduce cone programming. So first things first. Cone programming is a term (short for second-order cone program (SOCP)) is a convex optimization problem of the following form (1) where matrices fall in and vectors . On the […]