Lecture

Optimization Methods

Related lectures (29)

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

Covers the basics of constrained optimization, including tangent directions, trust-region subproblems, and necessary optimality conditions.

Approximation Algorithms

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

Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Quadratic Penalty Methods: Sound Problems

Explores Quadratic Penalty Methods for optimization with enforced constraints using penalty functions.

Dynamic Programming: Rod Cutting and Matrix Chain Multiplication

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

Introduction to Optimization

Introduces linear algebra, calculus, and optimization basics in Euclidean spaces, emphasizing the power of optimization as a modeling tool.

Nonlinear Programming: Part I

Covers the fundamentals of Nonlinear Programming and its applications in Optimal Control, exploring techniques, examples, optimality definitions, and necessary conditions.

Newton's Method: Optimization Techniques

Explores optimization techniques like gradient descent, line search, and Newton's method for efficient problem-solving.

Nonlinear Optimization Methods

Covers methods for solving nonlinear optimization problems, including direct search, Newton-Raphson, and branch and bound.

Optimization Problems: Greedy Algorithms

Explores optimization problems and greedy algorithms to find the best solutions efficiently.

Optimization Methods in Machine Learning

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

Optimisation in Energy Systems

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

Semi-Definite Programming

Covers semi-definite programming and optimization over positive semidefinite cones.

Mathematics of Data: Computation Role

Explores the role of computation in data mathematics, focusing on iterative methods, optimization, estimators, and descent principles.

Convexity of Lovász Extension

Explores the convexity of Lovász extension and submodular function maximization, focusing on extending functions to convex sets and proving their convexity.

Linear Programming: Extreme Points

Explores extreme points in linear programming and the role of constraints in finding optimal solutions.

Linear Programming: Weighted Bipartite Matching

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

Quasi-Newton Methods

Introduces Quasi-Newton methods for optimization, explaining their advantages over traditional approaches like Gradient Descent and Newton's Method.

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.