5 of 5 written

Convex Optimization

The optimization that runs inside contact solvers and policy updates: convex sets, quadratic programs, duality, cones, and how solvers descend.

Part 0

Why convexity makes a problem solvable, and what the feasible set that contact and control solvers live in looks like.

Part 1

From least squares to constrained QP, the form a contact-impulse solve (SAP) and a control step both take.

Part 2

Lagrangian duality and KKT, where contact and joint forces appear as dual variables.

Part 3

Second-order cone programs and projecting a force onto the Coulomb friction cone.

Part 4

How a solver actually reaches the optimum, and why the method sets the speed of PGS, Newton, and interior-point.