Lectures related to Primal-dual Methods for Composite Minimization

Primal-dual optimization: Theory and Computation

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

Primal-dual Optimization: Extra-Gradient Method

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

Optimality Conditions in Linear Optimization

Covers optimality conditions, strong duality, and complementarity slackness in linear optimization.

Primal-dual Optimization III: Lagrangian Gradient Methods

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

Linear Programming: Weighted Bipartite Matching

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

Primal-dual Optimization: Fundamentals

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

Quadratic Penalty Methods: Sound Problems

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

Linear Programming Techniques in Reinforcement Learning

Covers the linear programming approach to reinforcement learning, focusing on its applications and advantages in solving Markov decision processes.

Nonlinear Programming: Part I

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

Primal-dual Optimization: Methods and Applications

Explores primal-dual optimization methods, algorithms, convergence, and applications in nonconvex optimization and image deconvolution.

Hedging for LPs

Covers the concept of hedging for Linear Programs and the simplex method, focusing on minimizing costs and finding optimal solutions.

Introduction to Optimization

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

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Quadratic Penalty Methods: Concepts and Algorithms

Explores quadratic penalty methods for nonconvex-concave optimization problems and introduces primal-dual algorithms with penalty functions.

Projected Gradient Descent and Quadratic Penalty

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

Optimization Methods: Theory Discussion

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

KKT for convex problems and Slater's CQ

Covers the KKT conditions and Slater's condition in convex optimization problems.

KKT and Convex Optimization

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

Optimal Decision Making: Sensitivity Analysis

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.