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Probabilistic Analysis of an InfeasibleInteriorPoint Algorithm for Linear Programming
, 1998
"... We consider an infeasibleinteriorpoint algorithm, endowed with a finite termination scheme, applied to random linear programs generated according to a model of Todd. Such problems have degenerate optimal solutions, and possess no feasible starting point. We use no information regarding an optimal ..."
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Cited by 12 (3 self)
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We consider an infeasibleinteriorpoint algorithm, endowed with a finite termination scheme, applied to random linear programs generated according to a model of Todd. Such problems have degenerate optimal solutions, and possess no feasible starting point. We use no information regarding an optimal
Local Convergence of PredictorCorrector InfeasibleInteriorPoint Algorithms for SDPs and SDLCPs
 Mathematical Programming
, 1997
"... . An example of SDPs (semidefinite programs) exhibits a substantial difficulty in proving the superlinear convergence of a direct extension of the MizunoToddYe type predictorcorrector primaldual interiorpoint method for LPs (linear programs) to SDPs, and suggests that we need to force the genera ..."
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Cited by 58 (4 self)
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the generated sequence to converge to a solution tangentially to the central path (or trajectory). A MizunoToddYe type predictorcorrector infeasibleinteriorpoint algorithm incorporating this additional restriction for monotone SDLCPs (semidefinite linear complementarity problems) enjoys superlinear
On Superlinear Convergence of InfeasibleInteriorPoint Algorithms for Linearly Constrained Convex Programs
 Computational Optimization and Applications
, 1996
"... This note derives bounds on the length of the primaldual affine scaling directions associated with a linearly constrained convex program satisfying the following conditions: 1) the problem has a solution satisfying strict complementarity, 2) the Hessian of the objective function satisfies a certain ..."
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Cited by 2 (1 self)
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Introduction During the past few years, we have seen the appearance of many papers dealing with primaldual (feasible and infeasible) interior point algorithms for linear programs (LP), convex quadratic programs (QP), monotone linear complementarity problems (LCP) and monotone nonlinear complementarity
An Infeasible InteriorPoint Algorithm with Full NesterovTodd Step for Semidefinite Programming
"... This paper proposes an infeasible interiorpoint algorithm with full NesterovTodd step for semidefinite programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110– 1136, 2006). The polynomial bound coincides with that of infeasible interiorpoint methods for linear programmi ..."
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Cited by 5 (2 self)
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This paper proposes an infeasible interiorpoint algorithm with full NesterovTodd step for semidefinite programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110– 1136, 2006). The polynomial bound coincides with that of infeasible interiorpoint methods for linear
Polynomiality of an Inexact Infeasible Interior Point Algorithm for Semidefinite Programming
, 2001
"... In this paper we present a primaldual inexact infeasible interiorpoint algorithm for semidefinite programming problems (SDP). This algorithm allows the use of search directions that are calculated from the defining linear system with only moderate accuracy, and does not require feasibility to be m ..."
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Cited by 8 (3 self)
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In this paper we present a primaldual inexact infeasible interiorpoint algorithm for semidefinite programming problems (SDP). This algorithm allows the use of search directions that are calculated from the defining linear system with only moderate accuracy, and does not require feasibility
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
An Infeasible InteriorPoint Algorithm with fullNewton Step for Linear Optimization
"... In this paper we present an infeasible interiorpoint algorithm for solving linear optimization problems. This algorithm is obtained by modifying the search direction in the algorithm [8]. The analysis of our algorithm is much simpler than that of the algorithm [8] at some places. The iteration boun ..."
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In this paper we present an infeasible interiorpoint algorithm for solving linear optimization problems. This algorithm is obtained by modifying the search direction in the algorithm [8]. The analysis of our algorithm is much simpler than that of the algorithm [8] at some places. The iteration
An O(nL) infeasibleinteriorpoint algorithm for LCP with quadratic convergence
 Department of Mathematics, The University of Iowa, Iowa City, IA
, 1994
"... The MizunoToddYe predictorcorrector algorithm for linear programming is extended for solving monotone linear complementarity problems from infeasible starting points. The proposed algorithm requires two matrix factorizations and at most three backsolves per iteration. Its computational complexity ..."
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Cited by 21 (10 self)
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The MizunoToddYe predictorcorrector algorithm for linear programming is extended for solving monotone linear complementarity problems from infeasible starting points. The proposed algorithm requires two matrix factorizations and at most three backsolves per iteration. Its computational
A Superlinearly Convergent Infeasibleinteriorpoint Algorithm for Degenerate LCP
 DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF IOWA, IOWA CITY, IA
, 1995
"... A largestep infeasible pathfollowing method is proposed for solving general linear complementarity problems with sufficient matrices. If the problem has a solution the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. The algorithm generates poi ..."
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Cited by 17 (11 self)
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A largestep infeasible pathfollowing method is proposed for solving general linear complementarity problems with sufficient matrices. If the problem has a solution the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. The algorithm generates
A Second FullNewton Step O(n) Infeasible InteriorPoint Algorithm for Linear Optimization ∗
, 2005
"... In [4] the second author presented a new primaldual infeasible interiorpoint algorithm that uses fullNewton steps and whose iteration bound coincides with the best known bound for infeasible interiorpoint algorithms. Each iteration consists of a step that restores the feasibility for an intermed ..."
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Cited by 3 (2 self)
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In [4] the second author presented a new primaldual infeasible interiorpoint algorithm that uses fullNewton steps and whose iteration bound coincides with the best known bound for infeasible interiorpoint algorithms. Each iteration consists of a step that restores the feasibility
Results 1  10
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202,584