Lectures in course MATH-329: Continuous optimization

Covers weak and strong duality in optimization problems, focusing on Lagrange multipliers and KKT conditions.

Covers Projected Gradient Descent and Quadratic Penalty methods for optimization problems.

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

Covers projected gradient descent with a focus on quadratic penalty and optimality conditions.

Explores the challenges of quadratic penalties in optimization and the use of Augmented Lagrangian Methods (ALM) as a solution.

Covers the quadratic penalty method and augmented Lagrangian, including the setup and convergence of sequences.

Explores the Augmented Lagrangian Method with equality and inequality constraints in optimization, emphasizing the importance of slack variables.