Numerical solution of bilinear programming problems

Orlov, A. V.

doi:10.1134/s0965542508020061

Cited by 11 publications

(2 citation statements)

References 5 publications

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“…(x) This paper has worked two methods, assign instructors while keeping the students fixed (IA) and assign students while keeping the instructors fixed (SA) both of them come down to a linear optimization problem, 1 and 2 respectively. However, moving both instructors and students is no longer a linear but a bilinear optimization question (see [17,6]). This view will be further explored in future works.…”

Section: Finally We Definementioning

confidence: 99%

A big data based method for pass rates optimization in mathematics university lower division courses

Morales,

Chica,

Osorio

et al. 2018

Preprint

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In this paper an algorithm designed for large databases is introduced for the enhancement of pass rates in mathematical university lower division courses with several sections. Using integer programming techniques, the algorithm finds the optimal pairing of students and lecturers in order to maximize the success chances of the students' body. The students-lecturer success probability is computed according to their corresponding profiles stored in the data bases.

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Section: Finally We Definementioning

confidence: 99%

A big data based method for pass rates optimization in mathematics university lower division courses

Morales,

Chica,

Osorio

et al. 2018

Preprint

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show abstract

“…В [5] приводятся приближенные алгоритмы локального и глобального поисков оптимального решения в задачах билинейного программирования с несвязными переменными. Среди последних работ стоит отметить подход к решению билинейных задач, базирующийся на известном алгоритме внешних аппроксимаций.…”

Section: Introductionunclassified

Direct Method for Solving Bilinear Programming Problem

Матвеева

2021

Nauka teh.

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The bilinear programming problem is considered, where a column, which corresponds to one of the variables, is not fixed but can be chosen from a convex set. This problem is known as the Dantzig – Wolfe problem. Earlier, a modified support method was proposed to solve the problem, using the decomposition of the problem constraints of the Dantzig – Wolfe method. The author of the paper has developed a direct exact method for solving the formulated problem. The method is based on the idea of the solving a linear programming problem with generalized direct constraints and a general concept of an adaptive solution method. The notions of support, support plan, optimal and suboptimal (e-optimal) plan are introduced which is a given approximation of the objective function to the optimal plan of the problem. Criteria for optimality and suboptimality of the support plan have been formulated and have been proved in the paper. The search for the optimal solution is based on the idea of maximizing the increment of the objective function. This approach allows more fully to take into account the main target and structure of the problem. Improving a support plan consists of two parts: replacing the plan and replacing the support. To find a suitable direction, a special derived problem is solved while taking into account the main constraints of the problem. The replacement of the support is based on the search for the optimal plan of the dual problem. The method leads to an optimal solution to the problem in a finite number of iterations (in the case of a non-degenerate value).

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The Local and Global Searches in Bilevel Problems with a Matrix Game at the Lower Level

Orlov

Gruzdeva

2019

Mathematical Optimization Theory and Operations Research

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Numerical solution of bilinear programming problems

Cited by 11 publications

References 5 publications

A big data based method for pass rates optimization in mathematics university lower division courses

A big data based method for pass rates optimization in mathematics university lower division courses

Direct Method for Solving Bilinear Programming Problem

The Local and Global Searches in Bilevel Problems with a Matrix Game at the Lower Level

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