The cosine simplex algorithm

Corley, H. W.; Rosenberger, Jay M.; Yeh, Wei Chang; Sung, Tai-Kuan

doi:10.1007/s00170-004-2278-1

Cited by 35 publications

(34 citation statements)

References 9 publications

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“…The efficiency of the algorithm is tested by solving LPP for small scale problems using the Cosine Simplex method [3] and the proposed method. The following table 1shows a comparison between the numbers of constraints selected for two methods and it shows that the proposed method is very useful to solve the LPP with a minimum amount of computational efforts and time.…”

Section: Computational Resultsmentioning

confidence: 99%

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Selection of constraints with a new approach in linear programming problems

Sumathi¹,

Gangadharan²

2014

ams

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Linear programs (LP) play an important role in the theory and practice of optimization problems. Linear programming deals with problems such as maximising profits, minimising costs or ensuring you make the best use of available resources. While formulating a linear programming model, system analyst and researchers often tend to include all the possible constraints, although some of them may not be binding at the optimal solution. It is well known that, for most of the large scale LP problems, only a relatively small percentage of constraints are binding at the optimal solutions. Researchers have proposed methods which identify those constraints most likely to be tight at optimality. This paper proposes a new approach for finding solutions to LP problems by using a part of the constraints with the help of intercept and projection values of the each constraint. This method is more efficient when compared with the existing method. The developed algorithm is implemented by programming language Java and the computational results are presented. It shows that the proposed method reflects a significant decrease in the computational effort and is one of the best alternatives to select the necessary constraints prior to solving an LP problem.

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Section: Computational Resultsmentioning

confidence: 99%

“…The cosine criterion [3] plays a vital role more in the small scale problem than in the simplex but not in the large scale problem. The number of constraints selected is more in the large scale problem.…”

Section: Limitationsmentioning

confidence: 99%

Selection of constraints with a new approach in linear programming problems

Sumathi¹,

Gangadharan²

2014

ams

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“…More recently, Corley et al [14] developed a geometric prior active-set method for P called the cosine simplex method. At each active-set iteration , r a single violated constraint maximizing the cosine of the angle between i a and c is added to the operative set for r P .…”

Section: Introductionmentioning

confidence: 99%

Posterior Constraint Selection for Nonnegative Linear Programming

Corley¹,

Noroziroshan²,

Rosenberger³

2017

AJOR

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Posterior constraint optimal selection techniques (COSTs) are developed for nonnegative linear programming problems (NNLPs), and a geometric interpretation is provided. The posterior approach is used in both a dynamic and non-dynamic active-set framework. The computational performance of these methods is compared with the CPLEX standard linear programming algorithms, with two most-violated constraint approaches, and with previously developed COST algorithms for large-scale problems.

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“…The problem of efficiency has been addressed by reducing the number of simplex steps. One approach consists in bringing the initial solution closer to the optimal solution [1,3,9,16,19,40]. An outstanding instance of this approach is the work of Andersen et al [3], which combines an interior-point method and two simplex phases to solve LP problems in standard form.…”

Section: Introductionmentioning

confidence: 99%

A KKT Simplex Method for Efficiently Solving Linear Programs for Grasp Analysis Based on the Identification of Nonbinding Constraints

Mosso-Vázquez¹,

Juárez-Romero²,

Cruz-Chávez³

et al. 2014

CyS

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A one-phase efficient method to solve linear programming (LP) problems for grasp analysis of robotic hands is proposed. Our method, named as KKT Simplex method, processes free variables directly while choosing the entering and leaving variables, which makes it a one-phase method able to start at any point of the set of feasible solutions. Besides, the proposed method lowers the number of simplex steps by an angular pricing strategy to choose the entering variable. Moreover, the method reduces the size of an LP problem by the identification of nonbinding constraints that preserves the Karush-Kuhn-Tucker (KKT) cone. We developed the KKT Simplex method by incorporating to the well-known revised simplex method the following components: a method to process free variables, a pricing strategy, and an identification method. We solve LP problems of grasp analysis to test the efficiency and the one-phase nature of the proposed method.

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The cosine simplex algorithm

Cited by 35 publications

References 9 publications

Selection of constraints with a new approach in linear programming problems

Selection of constraints with a new approach in linear programming problems

Posterior Constraint Selection for Nonnegative Linear Programming

A KKT Simplex Method for Efficiently Solving Linear Programs for Grasp Analysis Based on the Identification of Nonbinding Constraints

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