Improved Full-Newton-Step Infeasible Interior-Point Method for Linear Complementarity Problems

Lešaja, Goran; Özen, Mustafa

doi:10.17535/crorr.2016.0001

Cited by 5 publications

(5 citation statements)

References 31 publications

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“…The pseudo-code of the new version of the algorithm is outlined in Figure 3 and the pseudo-code of the old version is outlined in [13]. Both versions are implemented in MATLAB and run on the desktop computer with Intel(R) core(TM) processor and 4 Gb of RAM running Windows 7 operating system.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The method is outlined in Figure 3 and throughout the text we referred to it as simply the Algorithm. The old version of the algorithm was discussed in [13,5]. In the old version of the method, each iteration consisted of one feasibility step and few centering steps (at most two) per iteration.…”

Section: Discussionmentioning

confidence: 99%

“…We present an Infeasible Interior-Point Method for monotone Linear Complementarity Problem (LCP ) which is an improved version of the algorithm given in [13]. In the earlier version, each iteration consisted of one feasibility step and few centering steps.…”

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confidence: 99%

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Untitled

2016

Croat. Oper. Res. Rev.

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Abstract. We present an Infeasible Interior-Point Method for monotone Linear Complementarity Problem (LCP ) which is an improved version of the algorithm given in [13]. In the earlier version, each iteration consisted of one feasibility step and few centering steps. The improved version guarantees that after one feasibility step, the new iterate is feasible and close enough to the central path thanks to the much tighter proximity estimate which is based on the new lemma introduced in [18]. Thus, the centering steps are eliminated. Another advantage of this method is the use of full-Newton-steps, that is, no calculation of the step size is required. The preliminary implementation and numerical results demonstrate the advantage of the improved version of the method in comparison with the old one.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Untitled

2016

Croat. Oper. Res. Rev.

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“…They are effective for solving large and ill-conditioned LCPs; their main drawbacks are the high cost per iteration and that they may not yield a good estimate of the solution when terminated early Morales et al (2007). Several algorithms have been proposed to lessen the required computations per step Lešaja et al (2012), Zangiabadi and Mansouri (2012). Yet, interior point algorithms remain computationally more expensive than active set algorithms Ferreau et al (2014).…”

Section: { }mentioning

confidence: 99%

An active set algorithm for a class of linear complementarity problems arising from rigid body dynamics

Sharaf¹

2016

Pak.j.stat.oper.res.

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An active set algorithm is introduced for positive definite and positive semi definite linear complementarity problems. The proposed algorithm is composed of two phases. Phase 1, the feasibility phase and phase 2, the optimality phase. In phase 1, the ellipsoid method is employed to test for feasibility and provide an advanced starting point if the problem is feasible. Providing such a warm start permits a good estimate of the active set. In phase 2, a criterion based on the complementarity condition is used to detect the working set per iteration until optimality is reached. This criterion leads to a valuable reduction in the size of the problem solved per iteration to obtain a search direction. Numerical examples are solved to illustrate the performance of the algorithm and a practical example in rigid body dynamics is solved to demonstrate the usage of the algorithm to solve such problems.

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“…The less module provides an overview of the development of the linear programming problem, linear programming model, theory of linear programming, counting vertices -enumeration method, geometric method, 2_ D, simplex method, Charnes' M-method [15], the two-phase simplex method [15], and finally, the method of interior points [9,10]. Software that aided learning linear programming included Excel Solver, Lindo, Winqsb and Simplex apple.…”

Section: Introductionmentioning

confidence: 99%

Research and evaluation of the effectiveness of e-learning in the case of linear programming

Miletić

Lešaja

2016

Croat. Oper. Res. Rev.

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Abstract. The paper evaluates the effectiveness of the e-learning approach to linear programming. The goal was to investigate how proper use of information and communication technologies (ICT) and interactive learning helps to improve high school students' understanding, learning and retention of advanced non-curriculum material. The hypothesis was that ICT and e-learning is helpful in teaching linear programming methods. In the first phase of the research, a module of lessons for linear programming (LP) was created using the software package Loomen Moodle and other interactive software packages such as Geogebra. In the second phase, the LP module was taught as a short course to two groups of high school students. These two groups of students were second-grade students in a Croatian high school. In Class 1, the module was taught using ICT and e-learning, while the module was taught using classical methods in Class 2. The action research methodology was an integral part in delivering the course to both student groups. The sample student groups were carefully selected to ensure that differences in background knowledge and learning potential were statistically negligible. Relevant data was collected while delivering the course. Statistical analysis of the collected data showed that the student group using the e-learning method produced better results than the group using a classical learning method. These findings support previous results on the effectiveness of e-learning, and also establish a specific approach to e-learning in linear programming.

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Improved Full-Newton-Step Infeasible Interior-Point Method for Linear Complementarity Problems

Cited by 5 publications

References 31 publications

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An active set algorithm for a class of linear complementarity problems arising from rigid body dynamics

Research and evaluation of the effectiveness of e-learning in the case of linear programming

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