Deepest point of a polyhedron and linear programming

DOI10.1080/02331934.2012.756877zbMath1311.90072OpenAlexW2081321954MaRDI QIDQ4981863

Ján Plesník

Publication date: 20 March 2015

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2012.756877

zbMATH Keywords

linear programminginterior point methodlinear inequalitiesbad examplesball centredeepest point of polyhedron

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Linear programming (90C05) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08) Interior-point methods (90C51)

Uses Software

• Matlab
• Optimization Toolbox

Cites Work

• The sagitta method for solving linear programs
• Zonotopes and the LP-Newton method
• Finding the orthogonal projection of a point onto an affine subspace
• Note on implementing the new sphere method for LP using matrix inversions sparingly
• An efficient simplex type algorithm for sparse and dense linear programs.
• A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs
• On Mehrotra-Type Predictor-Corrector Algorithms
• A Polynomial Predictor-Corrector Trust-Region Algorithm for Linear Programming
• Linear Programming in Linear Time When the Dimension Is Fixed
• A Strongly Polynomial Algorithm for a Special Class of Linear Programs
• Toward Probabilistic Analysis of Interior-Point Algorithms for Linear Programming
• On the solution of determinantal systems of linear inequalities
• A strongly polynomial algorithm for a new class of linear inequalities¹

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