Lectures related to Lagrangian Duality: Theory and Applications

Lagrangian Duality: Convex Optimization

Explores Lagrangian duality in convex optimization, transforming problems into min-max formulations and discussing the significance of dual solutions.

Linear Programming: Weighted Bipartite Matching

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

Convex Optimization Problems: Theory and Applications

Explores convex optimization problems, optimality criteria, equivalent problems, and practical applications in transportation and robotics.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Convex Optimization: Generalized Inequalities

Explores problems with generalized inequalities in convex optimization and the equivalence between SOCP and SDP.

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.

Duality in Linear Programming

Explores the concept of duality in linear programming, discussing the relationship between primal and dual problems.

Linear Programming Duality

Explores Linear Programming Duality, covering weak duality, strong duality, Lagrange multipliers interpretation, and optimization constraints.

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.

Convex Optimization Problems: Standard Form

Covers convex optimization problems, transformation to standard form, and optimality criteria for differentiable objectives.

Optimization Problems: Standard Form

Explores optimization problems in standard form, convex optimization, and optimality criteria.

Optimal Decision Making: Sensitivity Analysis

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

Linear Programming: Two-phase Simplex Algorithm

Covers the application of the two-phase Simplex algorithm to solve linear programming problems.

Convex Optimization: Farkas' Lemma

Covers Farkas' lemma, exploring the relationship between linear programs and the conditions for its validity.

Semi-Definite Programming

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

Linear Optimization: Auxiliary Problem

Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.

Convex Optimization: Dual Cones

Explores dual cones, generalized inequalities, SDP duality, and KKT conditions in convex optimization.

Optimization Methods: Theory Discussion

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

Convex Optimization: Self-dual Cones

Explores self-dual cones in convex optimization and their applications in various optimization problems.

Linear Optimization: Finding Initial BFS

Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.