Lectures related to Discrete Optimization: The Curse of Dimensionality

Energy System Modelling: Overview and Optimization Problems

Covers energy system modelling, optimization, scenarios, predictions, complexities, and controversies in energy models.

Linear Programming: Optimization and Constraints

Explores linear programming optimization with constraints, Dijkstra's algorithm, and LP formulations for finding feasible solutions.

Optimization: Classical Problems

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

The Backpack Problem

Introduces the backpack problem, a discrete optimization problem with constraints and algorithms to solve it.

Simplex Algorithm: Tableau

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

Dynamic Programming: Knapsack

Explores dynamic programming for the Knapsack problem, discussing strategies, algorithms, NP-hardness, and time complexity analysis.

Integer Optimization: Theory and Applications

Covers the fundamentals of integer optimization, including integer programming, dynamic programming, and approximation algorithms.

Elements of computational complexity

Covers classical and quantum computational complexity concepts and implications.

Knapsack Problem: Optimization and Traveling Salesman

Explores the knapsack problem and the traveling salesman problem with a focus on optimization algorithms.

Complexity Classes: P and NP

Explores complexity classes P and NP, highlighting solvable and verifiable problems, including NP-complete challenges.

Cutset Formulation: MST Problem

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

Dynamic Programming: Rod Cutting and Matrix Chain Multiplication

Covers dynamic programming techniques for solving the rod cutting and matrix chain multiplication problems.

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Solving Parity Games in Practice

Explores practical aspects of solving parity games, including winning strategies, algorithms, complexity, determinism, and heuristic approaches.

Convex Polyhedra and Linear Programs

Explores convex polyhedra, linear programs, and their optimization importance.

Subquadratic Attention Mechanisms: State Space Models Overview

Covers subquadratic attention mechanisms and state space models, focusing on their theoretical foundations and practical implementations in machine learning.

Approximation Algorithms

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

Optimization Algorithms

Covers optimization algorithms, convergence properties, and time complexity of sequences and functions.

Complex Systems: Critical Phenomena

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

Optimal Power Flow Solvers: Next Generation Advancements

Explores advancements in optimal power flow solvers, focusing on multiperiod and security-constrained optimization.