Energy System Modelling: Overview and Optimization Problems

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Minimum Spanning Trees: Prim's Algorithm

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

Complex Systems: Critical Phenomena

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Introduction to Shortest Path

Introduces the concept of shortest path, discussing weighted paths, Hamiltonian paths, and path optimization algorithms.

Approximation Algorithms

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

Optimization: Classical Problems

Covers classical optimization problems, brute force algorithms, and integer linear optimization.

Connect Four: Alpha-Beta Pruning and Monte-Carlo Tree Search

Explores solving Connect Four using game theory and algorithms for optimal strategy in minimum time.

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.

Simplex Algorithm: Tableau

Covers the main idea behind the Simplex algorithm and explains the Tableau method for solving linear programming problems.

Optimal Decision Making: Exercises and Applications

Covers exercises on optimal decision making, including minimizing costs and optimizing transportation networks.

Optimization Methods: Theory Discussion

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