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12
Implementation of interior point methods for large scale linear programming.” Interiorpoint methods of mathematical programming
, 1996
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A simplified homogeneous and selfdual linear programming algorithm and its implementation
 Annals of Operations Research
, 1996
"... 1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x ..."
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Cited by 62 (5 self)
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1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x
Multiple centrality corrections in a primaldual method for linear programming
 Computational Optimization and Applications
, 1996
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Presolve analysis of linear programs prior to applying an interior point method
 INFORMS Journal on Computing
, 1997
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Interior Point Trajectories in Semidefinite Programming
 SIAM Journal on Optimization
, 1996
"... In this paper we study interior point trajectories in semidefinite programming (SDP) including the central path of an SDP. This work was inspired by the seminal work by Megiddo on linear programming trajectories [15]. Under an assumption of primal and dual strict feasibility, we show that the primal ..."
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Cited by 38 (0 self)
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In this paper we study interior point trajectories in semidefinite programming (SDP) including the central path of an SDP. This work was inspired by the seminal work by Megiddo on linear programming trajectories [15]. Under an assumption of primal and dual strict feasibility, we show that the primal and dual central paths exist and converge to the analytic centers of the optimal faces of, respectively, the primal and the dual problems. We consider a class of trajectories that are similar to the central path, but can be constructed to pass through any given interior feasible point and study their convergence. Finally, we study the first order derivatives of these trajectories and their convergence. We also consider higher order derivatives associated with these trajectories.
A Computational View of InteriorPoint Methods for Linear Programming
 IN: ADVANCES IN LINEAR AND INTEGER PROGRAMMING
, 1994
"... Many issues that are crucial for an efficient implementation of an interior point algorithm are addressed in this paper. To start with, a prototype primaldual algorithm is presented. Next, many tricks that make it so efficient in practice are discussed in detail. Those include: the preprocessing te ..."
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Cited by 16 (10 self)
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Many issues that are crucial for an efficient implementation of an interior point algorithm are addressed in this paper. To start with, a prototype primaldual algorithm is presented. Next, many tricks that make it so efficient in practice are discussed in detail. Those include: the preprocessing techniques, the initialization approaches, the methods of computing search directions (and lying behind them linear algebra techniques), centering strategies and methods of stepsize selection. Several reasons for the manifestations of numerical difficulties like e.g.: the primal degeneracy of optimal solutions or the lack of feasible solutions are explained in a comprehensive way. A motivation for obtaining an optimal basis is given and a practicable algorithm to perform this task is presented. Advantages of different methods to perform postoptimal analysis (applicable to interior point optimal solutions) are discussed. Important questions that still remain open in the implementations of i...
Interior Point Algorithms For Linear Complementarity Problems Based On Large Neighborhoods Of The Central Path
 SIAM J. on Optimization
, 1998
"... In this paper we study a firstorder and a highorder algorithm for solving linear complementarity problems. These algorithms are implicitly associated with a large neighborhood whose size may depend on the dimension of the problems. The complexity of these algorithms depends on the size of the neig ..."
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Cited by 16 (3 self)
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In this paper we study a firstorder and a highorder algorithm for solving linear complementarity problems. These algorithms are implicitly associated with a large neighborhood whose size may depend on the dimension of the problems. The complexity of these algorithms depends on the size of the neighborhood. For the first order algorithm, we achieve the complexity bound which the typical largestep algorithms possess. It is wellknown that the complexity of largestep algorithms is greater than that of shortstep ones. By using highorder power series (hence the name highorder algorithm), the iteration complexity can be reduced. We show that the complexity upper bound for our highorder algorithms is equal to that for shortstep algorithms. Key Words: Interior point algorithm, Highorder power series, Large neighborhood, Large step, Complexity, Linear complementarity problem. Abbreviated Title: Interior point algorithms based on large neighborhoods AMS(MOS) subject classifications: 90...
Mixed semidefinitequadraticlinear programs
 in Recent Advances in LMI Methods for Control
, 2000
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Some disadvantages of a Mehrotratype primaldual corrector interior point algorithm for linear programming
 Numerical Analysis Group, Oxford University Computing Laboratory
, 2005
"... Employing a new primaldual corrector algorithm, we investigate the impact that corrector directions may have on the convergence behaviour of predictorcorrector methods. The PrimalDual Corrector (pdc) algorithm that we propose computes on each iteration a corrector direction in addition to the dir ..."
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Cited by 4 (0 self)
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Employing a new primaldual corrector algorithm, we investigate the impact that corrector directions may have on the convergence behaviour of predictorcorrector methods. The PrimalDual Corrector (pdc) algorithm that we propose computes on each iteration a corrector direction in addition to the direction of the standard primaldual pathfollowing interior point method [9, 22] for Linear Programming (lp), in an attempt to improve performance. The new iterate is chosen by moving along the sum of these directions, from the current iterate. This technique is similar to the construction of Mehrotra’s highly popular predictorcorrector algorithm [14]. We present examples, however, that show that the pdc algorithm may fail to converge to a solution of the lp problem, in both exact and finite arithmetic, regardless of the choice of stepsize that is employed. The cause of this bad behaviour is that the correctors exert too much influence on the direction in which the iterates move.
CostEffective Sulphur Emission Reduction Under Uncertainty
 International Institute for
, 1994
"... The problem of reducing SO 2 emissions in Europe is considered. The costs of reduction are assumed to be uncertain and are modeled by a set of possible scenarios. A meanvariance model of the problem is formulated and a specialized computational procedure is developed. The approach is applied to the ..."
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Cited by 3 (1 self)
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The problem of reducing SO 2 emissions in Europe is considered. The costs of reduction are assumed to be uncertain and are modeled by a set of possible scenarios. A meanvariance model of the problem is formulated and a specialized computational procedure is developed. The approach is applied to the transboundary air pollution model with realworld data. Keywords: Environment, Probabilistic programming, Interior point methods. iii iv CostEffective Sulphur Emission Reduction Under Uncertainty Anna Altman, Markus Amann, Ger Klaassen, Andrzej Ruszczy'nski, Wolfgang Schopp 1 Introduction Reducing the pollution in the environment has become one of the challenges of the present time in industrial countries, and especially in Europe. It is commonly agreed that action should be undertaken to stop the growth of emissions and eventually achieve a substantial reduction of depositions. One of the issues that attracts the attention of researchers and decisionmakers is the emission of sulphu...