# Optimization Algorithms

Canonical: https://manyspace.aporia.systems/topics/optimization-algorithms-mth-opt-240
Updated: 2026-10-13

Mathematics · Optimization · MTH-OPT-240

- Difficulty: 3 / 5
- Importance: 5 / 5
- Study time: 4–8.5 h

gradient descent, Newton's method, interior point methods, subgradient

## Why it matters

Choosing the best under constraints; central to operations research, ML training, engineering design and business resource allocation.

## Where it is used

Supply chains, pricing algorithms, portfolio optimization, neural network training, logistics, ad auctions.

## How you know you have learned it

Produce working code/model + convergence/validation/error analysis.

## What you need first

- [Gaussian Elimination](https://manyspace.aporia.systems/topics/gaussian-elimination-mth-linalg-155) (required)
- [3D Coordinates & Vectors](https://manyspace.aporia.systems/topics/3d-coordinates-vectors-mth-multc-168) (required)
- [Convex Sets & Functions](https://manyspace.aporia.systems/topics/convex-sets-functions-mth-opt-237) (required)

## What it opens

- [Gradient Descent in Machine Learning](https://manyspace.aporia.systems/topics/gradient-descent-in-machine-learning-aiml-opt-002)
- [Second-Order Methods](https://manyspace.aporia.systems/topics/second-order-methods-aiml-opt-008)

## Resources

- Introduction to Linear Programming — Bertsimas & Tsitsiklis
- Convex Optimization (Boyd & Vandenberghe) — Boyd & Vandenberghe
- Convex Optimization (Boyd & Vandenberghe) — Boyd & Vandenberghe