Optimal Power Flow: Constraints and Relaxations

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Optimization Methods: Theory Discussion

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

Initial BFS

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

Semi-Definite Programming

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

Convex Relaxation in Optimization

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

Convex Optimization Problems: Theory and Applications

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

Lagrangian Duality: Theory and Applications

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

Solving Integer Linear Programs

Covers solving integer linear programs graphically, algorithmically, and through optimization methods.

Discrete optimization: Knapsack

Explores modeling classic optimization problems as mixed integer linear problems, focusing on the knapsack problem and its applications.

Optimization Problems: Standard Form

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

Approximation Algorithms

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