Convex Sets: Theory and Applications

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Related lectures (28)

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Cones of convex sets

Explores optimization on convex sets, including KKT points and tangent cones.

Optimal Transport: Cyclically Monotone Sets

Covers cyclically monotone sets in optimal transport theory and their properties.

Convex Functions

Covers the definition of convex functions and their properties in optimization.

Convex Optimization: Sets and Functions

Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.

Unconstrained Optimization Theory

Explores unconstrained optimization theory, covering global and local minima, convexity, and gradient concepts.

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Convex Optimization: Introduction and Sets

Covers the fundamentals of convex optimization, including mathematical problems, minimizers, and solution concepts, with an emphasis on efficient methods and practical applications.

Introduction to Convexity

Introduces the key concepts of convexity and its applications in different fields.

Solving Linear Programs: SIMPLEX Method

Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.

Convex Sets: Mathematical Optimization

Introduces convex optimization, covering convex sets, solution concepts, and efficient numerical methods in mathematical optimization.