HPC Resources of South Ural State University

Dolganina, N.Yu.; Иванова, Е. В.; Bilenko, Roman; Rekachinsky, Alexander

doi:10.1007/978-3-031-11623-0_4

“…Using this program, we investigated the scalability of the apex method. The computational experiments were conducted on the "Tornado SUSU" computing cluster [51], whose specifications are shown in Table 1. As test problems, we used random synthetic LP problems generated by the program FRaGenLP [52].…”

Section: Implementation and Computational Experimentsmentioning

confidence: 99%

Apex Method: A New Scalable Iterative Method for Linear Programming

Sokolinsky¹,

Sokolinskaya²

2023

Preprint

0

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The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact solution of linear programming problem. The optimal path refers to a path of minimum length according to the Euclidean metric. The apex method is based on the predictor-corrector framework and proceeds in two stages: quest (predictor) and target (corrector). The quest stage calculates a rough initial approximation of linear programming problem. The target stage refines the initial approximation with a given precision. The main operation used in the apex method is an operation that calculates the pseudoprojection, which is a generalization of the metric projection to a convex closed set. This operation is used both in the quest stage and in the target stage. A parallel algorithm using a Fejér mapping to compute the pseudoprojection is presented. An analytical estimation of the parallelism degree of this algorithm is obtained. Also, an algorithm implementing the target stage is given. The convergence of this algorithm is proven. An experimental study of the scalability of the apex method on a cluster computing system is described. The results of applying the apex method to solve problems from the Netlib-LP repository are presented.

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“…Using this program, we investigated the scalability of the apex method. The computational experiments were conducted on the "Tornado SUSU" computing cluster [74], whose specifications are shown in Table 1. As test problems, we used random synthetic LP problems generated by the program FRaGenLP [75].…”

Section: Implementation and Computational Experimentsmentioning

confidence: 99%

Apex Method: A New Scalable Iterative Method for Linear Programming

Sokolinsky¹,

Sokolinskaya²

2023

Preprint

0

View full text Add to dashboard Cite

The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact solution of linear programming problem. The optimal path refers to a path of minimum length according to the Euclidean metric. The apex method is based on the predictor-corrector framework and proceeds in two stages: quest (predictor) and target (corrector). The quest stage calculates a rough initial approximation of linear programming problem. The target stage refines the initial approximation with a given precision. The main operation used in the apex method is an operation that calculates the pseudoprojection, which is a generalization of the metric projection to a convex closed set. This operation is used both in the quest stage and in the target stage. A parallel algorithm using a Fejér mapping to compute the pseudoprojection is presented. An analytical estimation of the parallelism degree of this algorithm is obtained. Also, an algorithm implementing the target stage is given. The convergence of this algorithm is proven. An experimental study of the scalability of the apex method on a cluster computing system is described. The results of applying the apex method to solve problems from the Netlib-LP repository are presented.

show abstract

“…Using this program, we investigated the scalability of the apex method. The computational experiments were conducted on the "Tornado SUSU" computing cluster [51], whose specifications are shown in Table 1.…”

Section: Implementation and Computational Experimentsmentioning

confidence: 99%

Apex Method: A New Scalable Iterative Method for Linear Programming

Sokolinsky

¹

,

Sokolinskaya

²

2023

Mathematics

1

0

View full text Add to dashboard Cite

The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact solution of a linear programming problem. The optimal path refers to a path of the minimum length according to the Euclidean metric. The apex method is based on the predictor-–corrector framework and proceeds in two stages: quest (predictor) and target (corrector). The quest stage calculates a rough initial approximation of the linear programming problem. The target stage refines the initial approximation with a given precision. The main operation used in the apex method is an operation that calculates the pseudoprojection, which is a generalization of the metric projection to a convex closed set. This operation is used both in the quest stage and in the target stage. A parallel algorithm using a Fejér mapping to compute the pseudoprojection is presented. An analytical estimation of the parallelism degree of this algorithm is obtained. AlsoAdditionally, an algorithm implementing the target stage is given. The convergence of this algorithm is proven. An experimental study of the scalability of the apex method on a cluster computing system is described. The results of applying the apex method to solve problems from the Netlib-LP repository are presented.

show abstract

HPC Resources of South Ural State University

Cited by 8 publications

References 26 publications

Apex Method: A New Scalable Iterative Method for Linear Programming

Apex Method: A New Scalable Iterative Method for Linear Programming

Apex Method: A New Scalable Iterative Method for Linear Programming

Apex Method: A New Scalable Iterative Method for Linear Programming

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