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37,226
Superlinear convergence of the affine scaling algorithm
, 1993
"... In this paper we show that a variant of the longstep affine scaling algorithm (with variable stepsizes) is twostep superlinearly convergent when applied to general linear programming (LP) problems. Superlinear convergence of the sequence of dual estimates is also established. For homogeneous LP pr ..."
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In this paper we show that a variant of the longstep affine scaling algorithm (with variable stepsizes) is twostep superlinearly convergent when applied to general linear programming (LP) problems. Superlinear convergence of the sequence of dual estimates is also established. For homogeneous LP
Exercise 1. The affine scaling algorithm.
, 2002
"... (a) Implement in MATLAB a function affscale.m which performs the affine scaling algorithm (as per p.400 in [1]). The prototype for the function is [xstar,ubflag,fconv,xconv] = affscale(A,b,c,x0,tol,beta), where the inputs A, b, and c are the usual (standard form) LP parameters, x0 is an initial fea ..."
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(a) Implement in MATLAB a function affscale.m which performs the affine scaling algorithm (as per p.400 in [1]). The prototype for the function is [xstar,ubflag,fconv,xconv] = affscale(A,b,c,x0,tol,beta), where the inputs A, b, and c are the usual (standard form) LP parameters, x0 is an initial
Affine Scaling Algorithm Fails For Semidefinite Programming
 Mathematical Programming 83
, 1997
"... In this paper, we introduce an affine scaling algorithm for semidefinite programming, and give an example of a semidefinite program such that the affine scaling algorithm converges to a nonoptimal point. Both our program and its dual have interior feasible solutions, and unique optimal solutions wh ..."
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Cited by 6 (1 self)
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In this paper, we introduce an affine scaling algorithm for semidefinite programming, and give an example of a semidefinite program such that the affine scaling algorithm converges to a nonoptimal point. Both our program and its dual have interior feasible solutions, and unique optimal solutions
Limit Analysis with the Dual Affine Scaling Algorithm
 J. Comput. Appl. Math
, 1995
"... The collapse state of a rigid plastic material with the linearized Mises yield condition is computed. We use an infeasible point variant of the dual affine scaling algorithm for linear programming which is extremely efficient for this large sparse and ill conditioned problem. For a classical test pr ..."
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Cited by 5 (2 self)
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The collapse state of a rigid plastic material with the linearized Mises yield condition is computed. We use an infeasible point variant of the dual affine scaling algorithm for linear programming which is extremely efficient for this large sparse and ill conditioned problem. For a classical test
Superlinear PrimalDual Affine Scaling Algorithms for LCP
 Mathematics of Operations Research
, 1993
"... We describe an interiorpoint algorithm for monotone linear complementarity problems in which primaldual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Qorder up to (but not including) two. The technique is shown to ..."
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Cited by 6 (3 self)
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We describe an interiorpoint algorithm for monotone linear complementarity problems in which primaldual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Qorder up to (but not including) two. The technique is shown
I. I. Dikin’s convergence result for the affinescaling algorithm
, 1990
"... The affinescaling algorithm is an analogue of Karmarkar's linear programming algorithm that uses affine transformations instead of projective transformations. Although this variant lacks some of the nice properties of Karmarkar's algorithm (for example, it is probably not a polynomialti ..."
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Cited by 22 (0 self)
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The affinescaling algorithm is an analogue of Karmarkar's linear programming algorithm that uses affine transformations instead of projective transformations. Although this variant lacks some of the nice properties of Karmarkar's algorithm (for example, it is probably not a polynomial
Superlinear primaldual affine scaling algorithms for LCP
, 1993
"... We describe an interiorpoint algorithm for monotone linear complementarity problems in which primaldual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Qorder up to (but not including) two. The technique is shown to ..."
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We describe an interiorpoint algorithm for monotone linear complementarity problems in which primaldual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Qorder up to (but not including) two. The technique is shown
PrimalDual AffineScaling Algorithms Fail For Semidefinite Programming
, 1998
"... In this paper, we give an example of a semidefinite programming problem in which primaldual affinescaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithm can generate a sequence converging to a nonoptimal solution, and that, for the AHO directio ..."
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Cited by 4 (0 self)
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In this paper, we give an example of a semidefinite programming problem in which primaldual affinescaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithm can generate a sequence converging to a nonoptimal solution, and that, for the AHO
Convergence properties of Dikin’s affine scaling algorithm for nonconvex quadratic minimization
 J. Global Optim
, 2001
"... Abstract We study convergence properties of Dikin's affine scaling algorithm applied to nonconvex quadratic minimization. First, we show that the objective function value either diverges or converges Qlinearly to a limit. Using this result, we show that, in the case of box constraints, the ite ..."
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Cited by 4 (1 self)
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Abstract We study convergence properties of Dikin's affine scaling algorithm applied to nonconvex quadratic minimization. First, we show that the objective function value either diverges or converges Qlinearly to a limit. Using this result, we show that, in the case of box constraints
Results 1  10
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37,226