Lectures related to Convexifying Nonconvex Problems: SDP and SOCP Relaxations

Convex Relaxation in Optimization

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

Optimal Decision Making: Sensitivity Analysis

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

Optimization Methods: Theory Discussion

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

Linear Programming: Weighted Bipartite Matching

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

Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Duality: Economic Interpretation

Explores duality in linear programming, strong duality, complementary slackness, and the economic interpretation of dual variables as prices.

Energy System Modeling: Optimization and Performance Indicators

Explores energy system modeling using optimization techniques and performance indicators.

Lagrangian Duality: Theory and Applications

Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.

Convex Optimization Problems: Theory and Applications

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

Semi-Definite Programming

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

Cutset Formulation: MST Problem

Explores the cutset formulation for the MST Problem and Gomory Cutting Planes method.

Linear Optimization: Auxiliary Problem

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

Duality in Linear Programming

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

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.

Optimisation Problem: Solving by FM

Covers the modelling and optimization of energy systems, focusing on solving optimization problems with constraints and variables.

Convex Relaxation: Negative Type Theorems

Explores convex relaxation and negative type theorems in convex programs.

Linear Programming Basics

Introduces linear programming basics, including optimization problems, cost functions, simplex algorithm, geometry of linear programs, extreme points, and degeneracy.

Optimization Problems: Standard Form

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

Integer Programs: Optimization and Constraints

Explores integer programs, nonconvex optimization, constraints, and geometric aspects of linear programming for optimal solutions.