Convex analysis | Lemmas in linear algebra | Linear programming

Farkas' lemma

Farkas' lemma is a solvability theorem for a finite system of linear inequalities in mathematics. It was originally proven by the Hungarian mathematician Gyula Farkas.Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization (alternatively, mathematical programming). It is used amongst other things in the proof of the Karush–Kuhn–Tucker theorem in nonlinear programming.Remarkably, in the area of the foundations of quantum theory, the lemma also underlies the complete set of Bell inequalities in the form of necessary and sufficient conditions for the existence of a local hidden-variable theory, given data from any specific set of measurements. Generalizations of the Farkas' lemma are about the solvability theorem for convex inequalities, i.e., infinite system of linear inequalities. Farkas' lemma belongs to a class of statements called "theorems of the alternative": a theorem stating that exactly one of two systems has a solution. (Wikipedia).

Video thumbnail

Introduction to geometric invariant theory 1: Noncommutative duality - Ankit Garg

Optimization, Complexity and Invariant Theory Topic: Introduction to geometric invariant theory 1: Noncommutative duality Speaker: Ankit Garg Affiliation: Microsoft Research New England Date: June 5. 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Tropical Geometry - Lecture 9 - Tropical Convexity | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Video thumbnail

Fractional Perfect Matchings in Hypergraphs - Andrzej Rucinski

Andrzej Rucinski Adam Mickiewicz University in Polznan, Poland; Emory University November 15, 2010 A perfect matching in a k-uniform hypergraph H = (V, E) on n vertices is a set of n/k disjoint edges of H, while a fractional perfect matching in H is a function w : E → [0, 1] such that for

From playlist Mathematics

Video thumbnail

Gavril Farkas: Moduli spaces of odd theta characteristics

Farkas: Moduli spaces of odd theta characteristics I will discuss joint work with Verra concerning a complete birational classification of the moduli space of odd spin curves of genus g. In particular, for g smaller 12, we find explicit unirational parametrizations of the moduli space, by

From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

Video thumbnail

Sifaka Lemurs Make A Treacherous Journey For Food | BBC Earth

Sifaka lemurs in Madagascar have to make a perilous journey with babies on board to reach their next feeding area. Subscribe: http://bit.ly/BBCEarthSub Watch more: Planet Earth http://bit.ly/PlanetEarthPlaylist Blue Planet http://bit.ly/BluePlanetPlaylist Planet Earth II http://bit.ly

From playlist New On Earth: Wildlife, Nature and Science Documentaries

Video thumbnail

Water and Wine

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Problems, Paradoxes, and Sophisms

Video thumbnail

James Lee: Semi Definite Extended Formulations and Sums of Squares (Part 1)

The lecture was held within the framework of the Hausdorff Trimester Program: Combinatorial Optimization

From playlist HIM Lectures 2015

Video thumbnail

Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 3 Linear Algebra: Linear Transformations

Video thumbnail

Linear Algebra 9a: Introduction to Gaussian Elimination

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

Video thumbnail

Linear Algebra 9L: Gaussian Elimination Example 4

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

Video thumbnail

Linear Algebra 8e: A 3x3 Linear System

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

Video thumbnail

Determinant Zen

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 2 Linear Algebra: An In-Depth Course with a Focus on Applications

Video thumbnail

Alessandro Verra: On the universal abelian variety over A 5 and the slope of A 6

In the talk the universal family Ug, over the moduli space Ag of complex p.p. abelian varieties of dimension g, is considered. The unirationality of U5 is proven. The construction is used to study the perfect cone compactification of A6 and bound its slope. Joint work with G. Farkas. The

From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

Video thumbnail

Gavril Farkas: The uniformization of the moduli space of abelian 6-folds

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebraic and Complex Geometry

Video thumbnail

Hardness of Randomized Truthful Mechanisms for Combinatorial Auctions - Jan Vondrak

Jan Vondrak IBM Almaden March 26, 2012 The problem of combinatorial auctions is one of the basic questions in algorithmic mechanism design: how can we allocate/sell m items to n agents with private valuations of different combinations of items, so that the agents are motivated to reveal th

From playlist Mathematics

Video thumbnail

Linear Algebra 6j: Linear Systems for the Impatient

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

Video thumbnail

Preview: The Magic of Gaussian Quadrature - A Billion Times Better than the Next Best Thing

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

Video thumbnail

Linear Algebra Vignette 1a: Matrix Representation of a Linear Transformation

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Linear Algebra Vignettes

Video thumbnail

Alessandro Chiodo - Towards a global mirror symmetry (Part 1)

Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the i

From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten

Video thumbnail

Linear Algebra 9m: Gaussian Elimination Example 5

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

Related pages

Karush–Kuhn–Tucker conditions | Completeness (logic) | Convex optimization | Hyperplane separation theorem | Nonlinear programming | Slater's condition | Hyperplane | Local hidden-variable theory | Fourier–Motzkin elimination | Fredholm alternative | Mathematical optimization | Minimax theorem | Convex cone | Lemma (mathematics) | Dual linear program | Bell's theorem | Linear programming | Closed set