The Trouble with Quadratic Penalties: ALM as a Fix

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Optimization Methods: Theory Discussion

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

Optimization with Constraints: KKT Conditions

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

Optimisation in Energy Systems

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

Linear Programming: Weighted Bipartite Matching

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

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.

Linear Constraints: Elimination of Variables

Explains linear constraints and variable elimination in optimization problems, illustrating the process step by step.

Two-phase Simplex Algorithm: Introduction and Duality

Introduces the two-phase simplex algorithm and explores duality in linear programming.

Quadratic Penalty Methods: Sound Problems

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

Minimum Spanning Trees: Prim's Algorithm

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Primal-dual optimization: Theory and Computation

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