Lectures related to Quadratic Penalty Methods: Concepts and Algorithms

Primal-dual Optimization III: Lagrangian Gradient Methods

Explores primal-dual optimization methods, emphasizing Lagrangian gradient techniques and their applications in data optimization.

Semi-Definite Programming

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

Optimization Methods: Theory Discussion

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

Optimization Programs: Piecewise Linear Cost Functions

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

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Energy Systems Optimization

Explores energy systems modeling, optimization, and cost analysis for efficient operations.

Introduction to Optimization

Covers the basics of optimization, including historical perspectives, mathematical formulations, and practical applications in decision-making problems.

Linear Programming: Solving LPs

Covers the process of solving Linear Programs (LPs) using the simplex method.

Optimization with Constraints: KKT Conditions

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

Optimization Principles

Covers optimization principles, including linear optimization, networks, and concrete research examples in transportation.

Introduction to Optimization and Operations Research

Covers fundamental concepts of optimization and operations research, exploring real-world examples and key topics over a semester.

Initial BFS

Explores finding the initial Basic Feasible Solution (BFS) in a linear program.

Primal-dual optimization: Theory and Computation

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

Solving Linear Programs: SIMPLEX Method

Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.

Primal-dual Optimization: Fundamentals

Explores primal-dual optimization, minimax problems, and gradient descent-ascent methods for optimization algorithms.

Duality: Duality in Linear Optimization

Covers the concept of linear optimization and the duality relationship between primal and dual problems.

Projected Gradient Descent and Quadratic Penalty

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

Convex Relaxation in Optimization

Explores convexifying nonconvex problems through relaxation techniques, illustrated with total variation reconstruction examples.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Optimization with Constraints: KKT Conditions

Covers the optimization with constraints, focusing on the Karush-Kuhn-Tucker (KKT) conditions.