G
Gábor Pataki
Researcher at University of North Carolina at Chapel Hill
Publications - 48
Citations - 1676
Gábor Pataki is an academic researcher from University of North Carolina at Chapel Hill. The author has contributed to research in topics: Semidefinite programming & Linear programming. The author has an hindex of 21, co-authored 46 publications receiving 1532 citations. Previous affiliations of Gábor Pataki include University of Waterloo & Columbia University.
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Journal ArticleDOI
On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues
TL;DR: It is proved that clustering must occur at extreme points of the set of optimal solutions, if the number of variables is sufficiently large and a lower bound on the multiplicity of the critical eigenvalue is given.
Book ChapterDOI
The Geometry of Semidefinite Programming
TL;DR: In this article, the primal-dual pair of optimization problems is considered, where X and Y are Euclidean spaces with dim X ≥ dim Y and Y → X is its adjoint.
Book ChapterDOI
Strong Duality in Conic Linear Programming: Facial Reduction and Extended Duals
TL;DR: In this article, the authors give a simple and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual, and state a simple FRA and prove its correctness.
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Teaching Integer Programming Formulations Using the Traveling Salesman Problem
TL;DR: A simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem, where students can optimally solve instances with up to 70 cities in a few minutes by adding cuts from the stronger formulation to the weaker, but simpler one.
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On the Closedness of the Linear Image of a Closed Convex Cone
TL;DR: Very simple and intuitive necessary conditions are presented that unify, and generalize seemingly disparate, classical sufficientconditions such as polyhedrality of the cone, and Slater-type conditions.