Monte Carlo Chain: Motivation and Algorithm

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Set Cover: Integrality Gap

Explores the integrality gap concept in set cover and multiplicative weights algorithms.

Descent methods and line search: Finiteness of the line search algorithm

Explores the Wolfe conditions for line search algorithms and proves the finiteness of the line search parameter.

Ford-Fulkerson: a worked example

Demonstrates the Ford-Fulkerson algorithm through a step-by-step worked example.

Linear Programming: Solving LPs

Covers the process of solving Linear Programs (LPs) using the simplex method.

Branch & Bound: Optimization

Covers the Branch & Bound algorithm for efficient exploration of feasible solutions and discusses LP relaxation, portfolio optimization, Nonlinear Programming, and various optimization problems.

Simulation & Optimization: Poisson Process & Random Numbers

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Markov Chains and Algorithm Applications

Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.

Dynamic Programming: Bellman-Ford and Dijkstra

Explores dynamic programming with Bellman-Ford, Dijkstra, greedy strategies, and activity scheduling problems.

Choosing a Step Size

Explores choosing a step size in optimization on manifolds, including backtracking line-search and the Armijo method.

Optimization Methods

Covers the Newton's local method in Python using NumPy for optimization.