Introducing Interior-Point Methods for Introductory Operations Research Courses and/or Linear Programming Courses

Lešaja, Goran

doi:10.2174/1874243200903010001

Cited by 22 publications

(19 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We simplified the calculation of the step size by enforcing only the positivity requirement for the new iterate in which case the calculation of the step size is almost exactly the same as the minimal ratio test in SM. Based on this simplification, convergence is not guaranteed, but it works well in practice, and problems rarely occur for certain ill-conditioned problems [9].…”

Section: Interior-point Methods Used In the Third Learning Cyclementioning

confidence: 99%

“…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%

See 1 more Smart Citation

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

Miletić

Lešaja

2016

Croat. Oper. Res. Rev.

View full text Add to dashboard Cite

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.

show abstract

Section: Interior-point Methods Used In the Third Learning Cyclementioning

confidence: 99%

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.

View full text Add to dashboard Cite

show abstract

“…Two important groups of methods are ones which use (a) interior point methods [10], and (b) simplex method after the linearization of the linear fractional objective functions. Here we investigate the efficiency of the linearization methods which use goal programming and the simplex method to solve the model (1).…”

Section:   mentioning

confidence: 99%

Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

Perić

Babić

Omerović

2017

CRORR

View full text Add to dashboard Cite

Abstract. This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1) Taylor's polynomial linearization approximation, (2) the method of variable change, and (3) a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a) using the optimal value of the objective functions as the decision makers' aspirations, and (b) the decision makers' aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.

show abstract

“…or equivalently, 4 Let m ≤ m be the rank of A B . By row operations and permutation of columns, we can transform the system…”

Section: Complexitymentioning

confidence: 99%

A still simpler way of introducing interior-point method for linear programming

Mehlhorn

Saxena

2016

Computer Science Review

View full text Add to dashboard Cite

show abstract

Introducing Interior-Point Methods for Introductory Operations Research Courses and/or Linear Programming Courses

Cited by 22 publications

References 49 publications

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

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

Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

A still simpler way of introducing interior-point method for linear programming

Contact Info

Product

Resources

About