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Dual–primal algorithm for linear optimization

Wei Li
2013 Optimization Methods and Software  
In each step of the iteration, we trace a direction completely different from primal simplex method, dual simplex method, primal-dual method and interior point method.  ...  The new method is impervious to primal degeneracy and can reach a pair of exact primal and dual optimal solutions without purifying process.  ...  (University of Málaga, Spain) for helpful discussions. Project par-  ... 
doi:10.1080/10556788.2011.643889 fatcat:knc44rkne5ftdpxsxt5z2zywia

Numerical Experiments with an Interior-Exterior Point Method for Nonlinear Programming

Igor Griva
2004 Computational optimization and applications  
The paper shows that in certain cases when the interior point method (ipm) fails to achieve the solution with the high level of accuracy, the use of the exterior point method (epm) can remedy this situation  ...  The algorithm is based on the combination of interior and exterior point methods. The latter is also known as the primaldual nonlinear rescaling method.  ...  Among all variations of interior point methods related to sumt, the primal-dual interior point method is the most efficient.  ... 
doi:10.1023/b:coap.0000042029.73199.83 fatcat:ofl25puaevafhlvsorvsshtcuq

Cutting Plane Methods and Subgradient Methods [chapter]

John E. Mitchell
2009 Decision Technologies and Applications  
We discuss the use of interior point methods in a column generation scheme.  ...  Interior point methods have proven very successful at solving linear programming problems.  ...  In order to use a primal-dual interior point method, we need points with x, x 0 , s, and s 0 all strictly positive.  ... 
doi:10.1287/educ.1090.0064 fatcat:yc24hzo62rfyxaemsrwt6jed3a

Computational experience with a primal-dual interior point method for linear programming

Irvin J. Lustig, Roy E. Marsten, David F. Shanno
1991 Linear Algebra and its Applications  
A new comprehensive implementation of a primal-dual algorithm for linear programming is described.  ...  We discuss in detail a variety of computational issues concerning the primal-dual implementation and barrier methods for linear programming in general.  ...  INTRODUCTION The primal-dual interior point algorithm for linear programming was introduced by Megiddo [I5], who used logarithmic barrier methods to solve the primal and dual problems simultaneously.  ... 
doi:10.1016/0024-3795(91)90275-2 fatcat:uvxahp767vhwleo2ozw26ubeou

Degeneracy in interior point methods for linear programming: a survey

O. Güler, D. den Hertog, C. Roos, T. Terlaky, T. Tsuchiya
1993 Annals of Operations Research  
The publication of Karmarkar's paper has resulted in intense research activity into Interior Point Methods (IPMs) for linear programming.  ...  Roughly speaking, we shall deal with the effect of degeneracy on the following: the convergence of IPMs, the trajectories followed by the algorithms, numerical performance, and finding basic solutions.  ...  The affine scaling algorithm is regarded as a primal-interior dual-exterior point algorithm in the sense that it generates the pair (x, s(x)) of primal-interior-feasible solution and dualfeasible/infeasible  ... 
doi:10.1007/bf02096259 fatcat:wfohc5pjibbotho4z6bo6kzukq

On finding a vertex solution using interior point methods

Sanjay Mehrotra
1991 Linear Algebra and its Applications  
The proposed approach is tested by using a variation of the primal-dual interior point method, Our method is developed by taking a predictorcorrector approach.  ...  An approach is proposed to generate a vertex solution while using a primal-dual interior point method to solve linear programs. A controlled random perturbation is made to the cost vector.  ...  Development of the Basic Procedure Let {rk} be a sequence of points (generated by an interior point method) converging to a vertex solution v, which is the optimal solution of P(r).  ... 
doi:10.1016/0024-3795(91)90277-4 fatcat:qdwog7r7affu7pmmmxq5ud3jjy

An Improved Interior Point Algorithm for Quantile Regression

Pan Zhao, Shenghua Yu
2020 IEEE Access  
ACKNOWLEDGMENT The authors are deeply thankful to the editor and reviews for their valuable suggestions to improve the quality of this manuscript.  ...  Colombo and Gondzio [32] revisited the technique of multiple centrality correctors and presented further development of multiple centrality correctors for interior point methods.  ...  The OPF problem is solved by a primal-dual interior point method with multiple centrality corrections as a sequence of linearized trust region sub-problems.  ... 
doi:10.1109/access.2020.3012871 fatcat:ndwpjfhgsjau7c4iqkdgnlovym

Page 4073 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
The proposed ap- proach is tested by using a variation of the primal-dual interior point method. Our method is developed by taking a predictor- corrector approach.  ...  Summary: “An approach is proposed to generate a vertex solution while using a primal-dual interior point method to solve linear programs. A controlled random perturbation is made to the cost vector.  ... 

An Adaptive Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semidefinite Optimization

Behrouz Kheirfam
2014 Journal of Mathematical Modelling and Algorithms in Operations Research  
We present an adaptive full Nesterov-Todd step infeasible interior-point method for semidefinite optimization.  ...  Keywords Infeasible interior-point algorithm · Semidefinite optimization · Full Nesterov-Todd step · Polynomial complexity Mathematics Subject Classifications (2010) 90C51 · 90C22 X 0, B. Kheirfam ( )  ...  Darvay [2] proposed a full-Newton step primal-dual path-following interior-point algorithm for LO.  ... 
doi:10.1007/s10852-014-9257-9 fatcat:f3bwwkzsefh3ncxbv2k7wsualy

Primal Dual Affine Scaling on GPUs [article]

Nithish Divakar
2015 arXiv   pre-print
Here we present an implementation of Primal-Dual Affine scaling method to solve linear optimization problem on GPU based systems.  ...  A new CUDA friendly technique to solve the resulting symmetric positive definite subsystem is also developed.  ...  Also the work of Mehora [5] on implementation of primal-dual methods are encouraging.  ... 
arXiv:1502.03543v1 fatcat:rogh4jlt3jf37bsqojvzg7vcfy


Emmanuel Gbenga Dada, Effirul Ikhwan Ramlan
2018 Malaysian Journal of Computer Science  
We propose Primal-Dual Interior Point Particle Swarm Optimization (pdPSO) to resolve the shortcomings of a standard PSO without the limitations of the IPM methods.  ...  We applied the Primal Dual procedure to each particle in a finite number of iterations, and fed the PSO with the its output.  ...  PRIMAL DUAL INTERIOR POINT METHOD The primal-dual interior-point (PDIP) method is an excellent example of an algorithm that uses constraintreduction methods.  ... 
doi:10.22452/mjcs.vol31no1.2 fatcat:pjdcjvt2ebck5jje6e2r3fx2p4

Page 5018 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
Summary: “We present a predictor-corrector algorithm for solving a primal-dual pair of linear programming problems.  ...  The corrector step uses a procedure employed in a feasible-interior-point algorithm.  ... 

Efficient solution of two-stage stochastic linear programs using interior point methods

J. R. Birge, D. F. Holmes
1992 Computational optimization and applications  
Several methods for improving the algorithmic efficiency of interior point algorithms by reducing the density of these matrices have been proposed in the literature.  ...  Solving deterministic equivalent formulations of two-stage stochastic linear programs using interior point methods may be computationally diflicult due to the need to factorize quite dense search direction  ...  The OSL interior point approach is a primal barrier method described in [21] .  ... 
doi:10.1007/bf00249637 fatcat:jmxh6p7ctbe3jm433s43xw5z6u

Efficient Algorithms for Checking Avoiding Sure Loss

Nawapon Nakharutai, Matthias C. M. Troffaes, Camila C. S. Caiado
2017 International Symposium on Imprecise Probabilities and Their Applications  
To assess our results, we compare the impact of these improvements on the simplex method and two interior point methods (affine scaling and primal-dual) on randomly generated sets of desirable gambles  ...  We also find that using our starting feasible point and extra stopping criterion considerably improves the performance of the primal-dual and affine scaling methods.  ...  Acknowledgments We would like to acknowledge support for this project from Development and Promotion of Science and Technology Talents Project (Royal Government of Thailand scholarship).  ... 
dblp:conf/isipta/NakharutaiTC17 fatcat:chhtcz5omvatpoxy3mivhvubda

A Note on the Behavior of Karmarkar's Potential Function in Linear Programming

J. N. Singh et. al.
2014 International Journal of Computational and Theoretical Statistics  
center of the simplex are zero; and the center of the simplex is a saddle point for the potential function.  ...  Finally, we prove that the β-superlevel set of the function G(x) is a convex set.  ...  From theoretical point of view it is a polynomial-time algorithm, which works on the interior of the feasible region.  ... 
doi:10.12785/ijcts/010102 fatcat:arp4htyaxzdevp6hnykq2arrom
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