Introduction to Optimization

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Related lectures (47)

Vector Spaces: Properties and Examples Log in to Mediaspace to watch this video

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Optimization Techniques: Gradient Descent and Convex Functions Log in to Mediaspace to watch this video

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Faster Gradient Descent: Projected Optimization Techniques Log in to Mediaspace to watch this video

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Proximal Gradient Descent: Optimization Techniques in Machine Learning Log in to Mediaspace to watch this video

Discusses proximal gradient descent and its applications in optimizing machine learning algorithms.

Optimization algorithms Log in to Mediaspace to watch this video

Covers optimization algorithms, focusing on Proximal Gradient Descent and its variations.

Variance Reduction: Strategies and Applications Log in to Mediaspace to watch this video

Discusses variance reduction techniques in stochastic simulation, focusing on allocation strategies and replica generation algorithms.

Semi-Definite Programming Log in to Mediaspace to watch this video

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

Linear Programming: Solving LPs Log in to Mediaspace to watch this video

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

Orthogonal Linear Maps Log in to Mediaspace to watch this video

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Decision Trees and Random Forests: Concepts and Applications Log in to Mediaspace to watch this video

Discusses decision trees and random forests, focusing on their structure, optimization, and application in regression and classification tasks.

Optimization Programs: Piecewise Linear Cost Functions Log in to Mediaspace to watch this video

Covers the formulation of optimization programs for minimizing piecewise linear cost functions.

Optimization Principles Log in to Mediaspace to watch this video

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

Dynamic Programming: How Many Ways to Make Change Log in to Mediaspace to watch this video

Demonstrates dynamic programming to find the number of ways to make change using different coin denominations.

Optimization in Engineering Log in to Mediaspace to watch this video

Explores optimization methods in engineering, covering decision variables, constraints, and various solving techniques.

Polynomial Optimization: SOS and SDP Log in to Mediaspace to watch this video

Explores Sum of Squares polynomials and Semidefinite Programming in Polynomial Optimization, enabling the approximation of non-convex polynomials with convex SDP.

Dynamic Programming: Knapsack Log in to Mediaspace to watch this video

Explores dynamic programming for the Knapsack problem, discussing strategies, algorithms, NP-hardness, and time complexity analysis.

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.

Two-phase Simplex Algorithm: Introduction and Duality Log in to Mediaspace to watch this video

Introduces the two-phase simplex algorithm and explores duality in linear programming.

The Geometry of Linear Optimization Log in to Mediaspace to watch this video

Delves into linear optimization formulation, capacity expansion, investment under taxation, and revenue management in various industries.

Convex Relaxation: Negative Type Theorems Log in to Mediaspace to watch this video

Explores convex relaxation and negative type theorems in convex programs.

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