Lectures related to Gradient Descent: Optimization and Constraints

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.

Linear Programming: Weighted Bipartite Matching

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

Formulation, Problem Transformations

Explores transforming optimization problems to meet algorithm requirements and make them equivalent.

Optimization without Constraints: Gradient Method

Covers optimization without constraints using the gradient method to find the function's minimum.

Linear Programming: Solving LPs

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

Optimization with Constraints: KKT Conditions Explained

Covers the KKT conditions for optimization with constraints, detailing their application and significance in solving constrained problems.

Nonlinear Optimization

Covers line search, Newton's method, BFGS, and conjugate gradient in nonlinear optimization.

Optimization Techniques: Stochastic Gradient Descent and Beyond

Discusses optimization techniques in machine learning, focusing on stochastic gradient descent and its applications in constrained and non-convex problems.

Optimization with Constraints: KKT Conditions

Covers the optimization with constraints, focusing on the Karush-Kuhn-Tucker (KKT) conditions.

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.