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We develop a natural variant of Dikin's affine-scaling method, first for semidefinite programming and then for hyperbolic programming in general.
An inequality for hyperbolic polynomials
Lars Garding · 1959
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Iterative solution to problems of linear and quadratic programming
I.I. Dikin · 1967
Earlier work this paper cites.
On the speed of an iterative process
I.I. Dikin · 1974
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A new polynomial-time algorithm for linear programming
N Karmarkar · 1984
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A variation on Karmarkar’s algorithm
N Megiddo · 1985
Earlier work this paper cites.
A modification of Karmarkar’s linear programming algorithm
Robert J Vanderbei, Marc S Meketon, and Barry A Freedman · 1986
Earlier work this paper cites.
Boundary behavior of interior point algorithms in linear programming
N Megiddo and M Shub · 1989
Earlier work this paper cites.
A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension
R C Monteiro, I Adler, and M G C Resende · 1990
Earlier work this paper cites.
Dikin’s convergence result for the affine-scaling algorithm
RJ Vanderbei and JC Lagarias · 1990
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Another derivation of the karmarkar direction for linear programming
Michael J Todd · 1991
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A simplified global convergence proof of the affine scaling algorithm
RDC Monteiro, T Tsuchiya, and Y Wang · 1993
Earlier work this paper cites.
Interior-point polynomial algorithms in convex programming
Yurii Nesterov and Arkadii Nemirovskii · 1994
Cited alongside, same era.
Global convergence of a long-step affine scaling algorithm for degenerate linear-programming problems
T Tsuchiya and M Muramatsu · 1995
Cited alongside, same era.
A polynomial primal-dual Dikin-type algorithm for linear programming
B Jansen, C Roos, and T Terlaky · 1996
Cited alongside, same era.
An O ( n L ) O(\sqrt{n}\,L) iteration bound primal-dual cone affine scaling algorithm for linear programming
Jos F Sturm and Shuzhong Zhang · 1996
Cited alongside, same era.
Hyperbolic polynomials and interior point methods for convex programming
Osman Güler · 1997
Cited alongside, same era.
Self-scaled barriers and interior-point methods for convex programming
A circular cone relaxation primal interior point algorithm for LP
Igor S Litvinchev · 2003
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The Lax conjecture is true
Adrian Lewis, Pablo Parrilo, and Motakuri Ramana · 2005
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Hyperbolic programs, and their derivative relaxations
James Renegar · 2006
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The primal-dual second-order cone approximations algorithm for symmetric cone programming
Chek Beng Chua · 2007
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Linear matrix inequality representation of sets
J William Helton and Victor Vinnikov · 2007
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Obstructions to determinantal representability
Petter Brändén · 2011
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Yu E Nesterov and Michael J Todd · 1997
Cited alongside, same era.
Potential-reduction methods in mathematical programming
Michael J Todd · 1997
Cited alongside, same era.
Polynomial primal-dual affine scaling algorithms in semidefinite programming
E de Klerk, C Roos, and T Terlaky · 1998
Cited alongside, same era.
Polynomial primal-dual cone affine scaling for semidefinite programming
Arjan B Berkelaar, Jos F Sturm, and Shuzhong Zhang · 1999
Cited alongside, same era.
A mathematical view of interior-point methods in convex optimization
James Renegar · 2001
Cited alongside, same era.
James Saunderson and Pablo A Parrilo · 2012
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Victor Vinnikov · 2012
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Central swaths
James Renegar · 2013
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Hyperbolicity cones of elementary symmetric polynomials are spectrahedral
Petter Brändén · 2014
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