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Fundamentals of Machine Learning: A Pythonic Introduction

Convex Optimization

Explore the fundamentals of convex optimization by understanding convex functions, their unique global minima, and key properties like supporting hyperplanes. This lesson helps you grasp why convex functions simplify optimization tasks in machine learning and introduces practical examples using Python code.

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What is convex optimization?

Convex optimization is a mathematical optimization technique that optimizes problems with convex objective functions and constraints.

Standard form

The standard form of a convex optimization problem is as follows:

min⁡xf0(x)s.t.fi(x)≤0i=1,2,…,mgj(x)=0j=1,2,…,k\begin{aligned} \min_{\bold x} \quad & f_0(\bold x)\\ \textrm{s.t.} \quad & f_i(\bold x)\le0 \quad & i=1,2,\dots,m\\ \quad & g_j(\bold x)=0 \quad & j=1,2,\dots,k \\ \end{aligned} ...