Variational Problems: Convexity and Coercivity

Related lectures (28)

Page 1 of 3

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers semi-definite programming and optimization over positive semidefinite cones.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Covers the proof of strong duality in optimization problems and provides examples of Rayleigh quotient optimization.

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.