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Concept

Constrained optimization

Related lectures (31)

Optimization Methods: Theory Discussion

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

Primal-dual optimization: Theory and Computation

Explores primal-dual optimization, conjugation of functions, strong duality, and quadratic penalty methods in data mathematics.

Equivalent formulation

Covers the concept of equivalent formulation in constrained optimization and explores the tangent cone.

Kernel SVM: Polynomial Expansion & Cover's Theorem

Explores polynomial expansion, high-dimensional spaces, Cover's Theorem, Lagrangian formulation, and practical SVM applications.

Duality: Duality in Linear Optimization MOOC: Optimization: principles and algorithms - Linear optimization

Covers the concept of linear optimization and the duality relationship between primal and dual problems.

Constrained Convex Optimization: Min-Max Formulation and Fenchel Conjugation

Explores constrained convex optimization with min-max formulation and Fenchel conjugation.

Optimal Control: Unconstrained and Constrained Problems

Explores optimal control in unconstrained and constrained problems, emphasizing the importance of sparsity.

Nonlinear Optimization Methods

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

Support Vector Machines: SVM Basics

Covers the basics of Support Vector Machines, focusing on hard-margin and soft-margin formulations.

Optimisation Problems: Methods and Constraints

Introduces optimisation problems, methods, and constraints for solving multi-dimensional problems with and without constraints.

Linear Constraints: Elimination of Variables MOOC: Optimization: principles and algorithms - Linear optimization

Explains linear constraints and variable elimination in optimization problems, illustrating the process step by step.

Linear Optimization: Directional Derivatives

Explores directional derivatives in linear optimization for function optimization along specific directions.

Linear Optimization: Active Constraints MOOC: Optimization: principles and algorithms - Linear optimization

Explores the significance of active constraints in linear optimization, showcasing how they influence the simplification of problems by focusing on relevant constraints.

Optimization Techniques: Convexity in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity and its implications for efficient problem-solving.

Optimality Conditions in Linear Optimization MOOC: Optimization: principles and algorithms - Linear optimization

Covers basic directions, slopes, reduced costs, optimality conditions, and a summary.

Primal-dual Optimization II

Explores primal-dual optimization methods, focusing on Lagrangian approaches and various methods like penalty, augmented Lagrangian, and splitting techniques.

Optimal Decision Making: Exercises and Applications Log in to Mediaspace to watch this video

Covers exercises on optimal decision making, including minimizing costs and optimizing transportation networks.

Constrained optimization: the basics Log in to Mediaspace to watch this video

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

Convex Optimization Tutorial: KKT Conditions Log in to Mediaspace to watch this video

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Linear Optimization: Fundamentals Log in to Mediaspace to watch this video

Covers the basics of linear optimization, including equations, polyhedrons, feasible directions, and optimal solutions.