Convex Optimization

Introduction of Convex Optimization

Ahmad Bazzi 2 months ago

Mathematical optimization is a problem that takes the following form (1)   where is a vector containing all the variables of the problem (2)   The function is referred to as the cost or the objective function. Moreover, the functions are referred to as constraint functions. In most cases, our […]

Strong Alternatives

Ahmad Bazzi 3 months ago

The above lecture is brought to you by Skillshare. In a previous post of mine, we introduced weak alternatives. As a small reminder, consider the following two sets (1)   and (2)   where (3)   is the dual function and is the domain of the problem. Since we did […]

Weak Alternatives

Ahmad Bazzi 3 months ago

Let us say we are interested in checking whether system hereby defined as (1)   is feasible or not. In other words, could we find a vector that satisfies set ? In many cases, it may turn out to be hard to answer the question by exhaustively searching all possible […]

Perturbation & Sensitivity Analysis

Ahmad Bazzi 4 months ago

In this lecture, we talk about Perturbation and Sensitivity Analysis. But what does that mean ? Well, consider our good old looking optimization problem that looks like this (1)   One way to tell how the above problem reacts to perturbation is to actually perturb it and check how its […]

Equivalent Reformulations

Ahmad Bazzi 4 months ago

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 ? […]