Gradient Descent: Optimization and Constraints

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Optimization Basics: Unconstrained Optimization and Gradient Descent

Covers optimization basics, including unconstrained optimization and gradient descent methods for finding optimal solutions.

Computing the Newton Step: GD as a Matrix-Free Way

Explores matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds.

Optimization Methods in Machine Learning

Explores optimization methods in machine learning, emphasizing gradients, costs, and computational efforts for efficient model training.

Introduction to Optimization

Covers the basics of optimization, including historical perspectives, mathematical formulations, and practical applications in decision-making problems.

Introduction to Optimization and Operations Research

Covers fundamental concepts of optimization and operations research, exploring real-world examples and key topics over a semester.

Optimisation in Energy Systems

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

Optimization Principles

Covers optimization principles, including linear optimization, networks, and concrete research examples in transportation.

Gradient Descent

Covers the concept of gradient descent in scalar cases, focusing on finding the minimum of a function by iteratively moving in the direction of the negative gradient.

Simplex Algorithm: Basics

Introduces the Simplex algorithm for solving flow problems and handling negative cost cycles.

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.