Duality: Lagrangian and Dual Problem

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Optimization Duality: Theory and Algorithms

Explores optimization duality, weak and strong duality, practical optimization algorithms, and challenges in nonconvex-concave problems.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Primal-dual Optimization: Fundamentals

Explores primal-dual optimization, minimax problems, and gradient descent-ascent methods for optimization algorithms.

Optimal Decision Making: Duality

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

Linear Optimization: Auxiliary Problem

Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.

Fenchel Conjugation: Basics and Applications

Introduces Fenchel conjugation, exploring its properties, examples, and applications in nonsmooth optimization problems and minimax formulations.

Duality: Economic Interpretation

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

Lagrangian Duality: Theory and Applications

Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.

Dual Space and Weak Convergence

Explores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.