Lecture

Variational Problems: Convexity and Coercivity

Related lectures (28)

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.

Explores Quadratic Penalty Methods for optimization with enforced constraints using penalty functions.

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Covers the formulation of optimization programs for minimizing piecewise linear cost functions.

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Discusses proximal gradient descent and its applications in optimizing machine learning algorithms.

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.