Concept

Dual system

Related lectures (32)

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.

Covers the application of the two-phase Simplex algorithm to solve linear programming problems.

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

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

Covers Lagrangian, dual function, dual problem, weak duality, and optimality.

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

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

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

Explores the weak formulation of linear elliptic partial differential equations and the concept of weak solutions in PDEs.

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Covers the definitions and properties of dual spaces and linear operators.

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

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

Covers dimension theorems for linear transformations, bijectivity, isomorphism, dual spaces, and canonical applications.

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

Explores the concept of duality in linear programming, discussing the relationship between primal and dual problems.

Covers the concept of functors, assigning morphisms and dual spaces in different categories.

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

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