What is it?
Minimize only over the points that satisfy constraints or : a budget, a physical limit, a probability that must sum to 1. The minimum can now sit on the boundary, where .
Formulas
Where it shows up in computing
Scheduling, routing and allocation are optimization under capacity and demand constraints.
A robot trajectory minimizes effort subject to dynamics, joint limits and obstacles.
Where is it used?
Computing topics reachable from here, through the chain of ideas that leads to them:
ℒ AI and machine learning
- Lagrange multipliers→Support vector machines★★★★★
- Lagrange multipliers→Regularization★★★★★
- Lagrange multipliers→Regularization→Deep learning★★★★★
- Lagrange multipliers→Regularization→Deep learning→Convolutional networks (CNNs)★★★★★
- Lagrange multipliers→Regularization→Deep learning→Generative models★★★★★
- Lagrange multipliers→Regularization→Deep learning→Neural ODEs★★★★★
What depends on it
This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.