Concept

Verdier duality

Related lectures (31)

Explores Linear Programming Duality, covering weak duality, strong duality, Lagrange multipliers interpretation, and optimization constraints.

Cup and Cap Product: Poincaré Duality

Explains the cup and cap product in algebraic topology and their relation to homology groups.

Support Vector Regression: Recap and Convex Optimization

Covers the recap of Support Vector Regression with a focus on convex optimization and its equivalence to Gaussian Process Regression.

Fresnel Coefficients TM Polarization

Discusses the Fresnel coefficients for TM polarization and their application to the solution.

Duality: Economic Interpretation

Explores duality in linear programming, strong duality, complementary slackness, and the economic interpretation of dual variables as prices.

Limits and Colimits: Understanding Categories

Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.

Optimization in Networks

Explores duality in network optimization problems with examples and step-by-step explanations.

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Duality and PBH Test in Multivariable Control

Explores duality, PBH test, observability, and exact discretization in multivariable control systems.

Local Global Duality

Explores local-global duality in lattices and joint equidistribution of CM points.

Certificates: Existence and Proving

Explores certificates, proving solution existence, constraints, and linear programming duality.

Duality, Constraint relaxation

Explores duality and constraint relaxation in optimization problems with practical examples.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Optimal Decision Making: Duality

Delves into duality in optimization, weak duality, cost certificates, and transforming non-linear programs into linear ones.

Linear Optimization: Finding Initial BFS

Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.

Weak and Strong Duality

Covers weak and strong duality in optimization problems, focusing on Lagrange multipliers and KKT conditions.

Distribution & Interpolation Spaces

Covers the concept of distributions with compact support and their interpolation spaces.

Proof of Strong Duality

Covers the proof of strong duality in optimization problems and provides examples of Rayleigh quotient optimization.

Linear Programming Duality

Covers linear programming duality and complementary slackness condition.

Elementary Properties of Model Categories

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.