Lectures related to Lagrange Multiplier and DuBois-Reymond Equation

Optimal Control: Unconstrained and Constrained Problems

Explores optimal control in unconstrained and constrained problems, emphasizing the importance of sparsity.

Covers the fundamentals of Nonlinear Programming and its applications in Optimal Control, exploring techniques, examples, optimality definitions, and necessary conditions.

Primal-dual optimization: Theory and Computation

Explores primal-dual optimization, conjugation of functions, strong duality, and quadratic penalty methods in data mathematics.

Calculus of Variations: Gradient Young Theorem

Covers the Gradient Young Theorem in the calculus of variations, discussing proofs and applications.

Optimization Methods: Lagrange Multipliers

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.

Stochastic Gradient Descent: Non-convex Optimization Techniques

Discusses Stochastic Gradient Descent and its application in non-convex optimization, focusing on convergence rates and challenges in machine learning.