Projective transformations for interior-point algorithms, and a superlinearly convergent algorithm for the w-center problem

DOI10.1007/BF01581277zbMath0792.90041MaRDI QIDQ2367917

Robert M. Freund

Publication date: 17 August 1993

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

zbMATH Keywords

Newton methodellipsoidanalytic centerweighted centerbarrier penaltyprojective transformation methodsw-center of a polyhedral system

Mathematics Subject Classification ID

Linear programming (90C05) Computational methods for problems pertaining to operations research and mathematical programming (90-08)

Related Items (7)

Sufficient weighted complementarity problems ⋮ Scaling, shifting and weighting in interior-point methods ⋮ A primal-dual interior-point method for linear programming based on a weighted barrier function ⋮ Primal-dual target-following algorithms for linear programming ⋮ Interior-point algorithms for a generalization of linear programming and weighted centring ⋮ Monotone variable-metric algorithm for linearly constrained nonlinear programming ⋮ Theoretical efficiency of a shifted-barrier-function algorithm for linear programming

Cites Work

• A monotonic projective algorithm for fractional linear programming
• A modification of Karmarkar's linear programming algorithm
• A new polynomial-time algorithm for linear programming
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• A polynomial-time algorithm, based on Newton's method, for linear programming
• Interior path following primal-dual algorithms. I: Linear programming
• Interior path following primal-dual algorithms. II: Convex quadratic programming
• Karmarkar's linear programming algorithm and Newton's method
• On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method
• A variation on Karmarkar’s algorithm for solving linear programming problems
• A Centered Projective Algorithm for Linear Programming
• The Nonlinear Geometry of Linear Programming. III Projective Legendre Transform Coordinates and Hilbert Geometry
• A variant of Karmarkar's linear programming algorithm for problems in standard form
• Optimization of “$\log x$” Entropy over Linear Equality Constraints
• A Method for the Parametric Center Problem, with a Strictly Monotone Polynomial-Time Algorithm for Linear Programming
• Convex Analysis
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