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A Superlinearly Convergent PrimalDual InfeasibleInteriorPoint Algorithm for Semidefinite Programming
 DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF IOWA, IOWA CITY, IA
, 1995
"... A primaldual infeasibleinteriorpoint pathfollowing algorithm is proposed for solving semidefinite programming (SDP) problems. If the problem has a solution, then the algorithm is globally convergent. If the starting point is feasible or close to being feasible, the algorithms finds an optimal s ..."
Abstract

Cited by 60 (9 self)
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A primaldual infeasibleinteriorpoint pathfollowing algorithm is proposed for solving semidefinite programming (SDP) problems. If the problem has a solution, then the algorithm is globally convergent. If the starting point is feasible or close to being feasible, the algorithms finds an optimal
Superlinear Convergence of InteriorPoint Algorithms for Semidefinite Programming
 Journal of Optimization Theory and Applications
, 1996
"... We prove the superlinear convergence of the primaldual infeasibleinteriorpoint pathfollowing algorithm proposed recently by Kojima, Shida and Shindoh and the present authors, under two conditions: (1) the SDP problem has a strictly complementary solution, and (2) the size of the central path nei ..."
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Cited by 20 (7 self)
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We prove the superlinear convergence of the primaldual infeasibleinteriorpoint pathfollowing algorithm proposed recently by Kojima, Shida and Shindoh and the present authors, under two conditions: (1) the SDP problem has a strictly complementary solution, and (2) the size of the central path
PrimalDual PathFollowing Algorithms for Semidefinite Programming
 SIAM Journal on Optimization
, 1996
"... This paper deals with a class of primaldual interiorpoint algorithms for semidefinite programming (SDP) which was recently introduced by Kojima, Shindoh and Hara [11]. These authors proposed a family of primaldual search directions that generalizes the one used in algorithms for linear programmin ..."
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Cited by 165 (12 self)
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This paper deals with a class of primaldual interiorpoint algorithms for semidefinite programming (SDP) which was recently introduced by Kojima, Shindoh and Hara [11]. These authors proposed a family of primaldual search directions that generalizes the one used in algorithms for linear
On PrimalDual PathFollowing Algorithms in Semidefinite Programming
, 1996
"... Interior point methods for semidefinite programming have recently been studied intensively, due to their polynomial complexity and practical efficiency. Most of these methods are extensions of linear programming algorithms. The primaldual central path following method for linear programming by Janse ..."
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convergence to target points on the central path is shown. Moreover, we show how to compute large dynamic target updates which still allow full Newton steps. Key words: interiorpoint method, primaldual method, pathfollowing, semidefinite programming. Running title: PathFollowing Methods for SDP. iii
InfeasibleInteriorPoint PrimalDual PotentialReduction Algorithms For Linear Programming
 SIAM Journal on Optimization
, 1995
"... . In this paper, we propose primaldual potentialreduction algorithms which can start from an infeasible interior point. We first describe two such algorithms and show that both are polynomialtime bounded. One of the algorithms decreases the TanabeToddYe primaldual potential function by a const ..."
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Cited by 21 (4 self)
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. In this paper, we propose primaldual potentialreduction algorithms which can start from an infeasible interior point. We first describe two such algorithms and show that both are polynomialtime bounded. One of the algorithms decreases the TanabeToddYe primaldual potential function by a
A PathFollowing InfeasibleInteriorPoint Algorithm for Linear Complementarity Problems
 Optimization Methods and Software
, 1993
"... We describe an infeasibleinteriorpoint algorithm for monotone linear complementarity problems that has polynomial complexity, global linear convergence, and local superlinear convergence with a Qorder of 2. Only one matrix factorization is required per iteration, and the analysis assumes only tha ..."
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Cited by 56 (10 self)
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We describe an infeasibleinteriorpoint algorithm for monotone linear complementarity problems that has polynomial complexity, global linear convergence, and local superlinear convergence with a Qorder of 2. Only one matrix factorization is required per iteration, and the analysis assumes only
INTERIOR PATH FOLLOWING PRIMALDUAL ALGORITHMS. PART I: LINEAR PROGRAMMING
, 1989
"... We describe a primaldual interior point algorithm for linear programming problems which requires a total of O(~fnL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the KarushKuhnTucker system of equations w ..."
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Cited by 199 (11 self)
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We describe a primaldual interior point algorithm for linear programming problems which requires a total of O(~fnL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the KarushKuhnTucker system of equations
PrimalDual InteriorPoint Methods for SelfScaled Cones
 SIAM Journal on Optimization
, 1995
"... In this paper we continue the development of a theoretical foundation for efficient primaldual interiorpoint algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are selfscaled (see [9]). The class of problems under consideration includes li ..."
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Cited by 206 (12 self)
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In this paper we continue the development of a theoretical foundation for efficient primaldual interiorpoint algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are selfscaled (see [9]). The class of problems under consideration includes
A Unified Analysis for a Class of LongStep PrimalDual PathFollowing InteriorPoint Algorithms for Semidefinite Programming
 MATH. PROGRAMMING
, 1998
"... We present a unified analysis for a class of longstep primaldual pathfollowing algorithms for semidefinite programming whose search directions are obtained through linearization of the symmetrized equation of the central path HP (XS) j [P XSP \Gamma1 + (PXSP \Gamma1 ) T ]=2 = ¯I, introduce ..."
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Cited by 23 (0 self)
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We present a unified analysis for a class of longstep primaldual pathfollowing algorithms for semidefinite programming whose search directions are obtained through linearization of the symmetrized equation of the central path HP (XS) j [P XSP \Gamma1 + (PXSP \Gamma1 ) T ]=2 = ¯I
Superlinear convergence of a symmetric primaldual pathfollowing algorithm for semidefinite programming
 SIAM JOURNAL ON OPTIMIZATION
, 1998
"... This paper establishes the superlinear convergence of a symmetric primaldual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primaldual optimal solution and that the size of the central path neighborhood tends to ..."
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Cited by 55 (5 self)
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This paper establishes the superlinear convergence of a symmetric primaldual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primaldual optimal solution and that the size of the central path neighborhood tends
Results 1  10
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521