# SVM optimality conditions

(1.1 hours to learn)

## Summary

Using Lagrange duality, we can formulate a set of conditions that characterize the optimal solution to the SVM objective. These conditions show that the weight vector is a linear combination of a (hopefully small) subset of the training points, those for which the margin constraint is tight.

## Context

This concept has the prerequisites:

- the support vector machine
- Langrange duality (The optimality conditions for SVMs are derived from the Lagrange dual.)
- KKT conditions (The optimality conditions are an instance of the KKT conditions.)

## Core resources (read/watch one of the following)

## -Free-

→ Stanford's Machine Learning lecture notes

Lecture notes for Stanford's machine learning course, aimed at graduate and advanced undergraduate students.

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ The Elements of Statistical Learning

A graudate-level statistical learning textbook with a focus on frequentist methods.

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 7.1, up to 7.1.1, pages 326-331

## See also

-No Additional Notes-