A decomposition approach to the solution of some integer programming problems with inexact data

Roshchin, V. A.; Semenova, N. V.; Sergiyenko, I.V.

doi:10.1016/0041-5553(90)90197-z

Cited by 2 publications

(3 citation statements)

References 4 publications

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“…, we conclude that the point set { } x k l is finite. Therefore, it is possible to select a stationary sequence, i.e., $l * such that " ³ = l l x x k l * , and no new constrain is added to (8) in the MP problem beginning with an l * . This is possible only when x X Î 2 .…”

Section: Decomposition Approach To Searching For Exact and Approximatmentioning

confidence: 99%

“…Continuing the studies reflected in [4][5][6][7][8][9][10], we present the results of developing and substantiating methods for exact and approximate solution of problems originating in studying complex integer optimization models with controlled and inexact initial data and based on their approximation by problems of a more simple structure. These methods are decomposition ones, they combine and use the ideas of relaxation [12], linearization [13], and Kelley cutting plane [14] methods.…”

Section: Introductionmentioning

confidence: 99%

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Methods of searching for guaranteeing and optimistic solutions to integer optimization problems under uncertainty

Semenova

2007

Cybern Syst Anal

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Section: Decomposition Approach To Searching For Exact and Approximatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Methods of searching for guaranteeing and optimistic solutions to integer optimization problems under uncertainty

Semenova

2007

Cybern Syst Anal

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“…E H; b E B; C, H, and B are convex polyhedra in R n, R mxn, and R m, respectively. The definition of inexact parameters by their possible value set makes it possible to consider problems corresponding to various modeled situations [96]. Thus, an inexact integer programming problem of the following form was considered:…”

Section: X*exmentioning

confidence: 99%

Some directions and results of research in mathematical programming and system analysis

Сергиенко¹

1995

Cybern Syst Anal

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This article reviews the research in informatics, optimization theory, and system analysis associated with the scientific interests of our well-known scientist and mathematician, V. S. Mikhalevich, and his closest students and followers. We should qualify at the outset that the article does not review the full body of work of Mikhalevich, and certainly not of all his students: their work is much too extensive and much too multifaceted for one survey article. Moreover, in optimization theory, for instance, the Kiev mathematical school includes directions represented by other widely known scientists, and again these are not treated in the present article. I have decided to focus only on the studies and the directions of research to which V. S. Mikhalevich attached particular significance, which to a certain extent characterize his scientific creativity, and which are widely acknowledged among experts in our country and abroad.The active development of research in mathematical programming and system analysis at the National Academy of Sciences of Ukraine began in the late 1950s and early 1960s, when the Computational Center of the Academy of Sciences of the Ukrainian SSR and a number of other scientific organizations in the country focused on the creation of new computers and computer software. At that time, Academician V. M. Glushkov organized in Kiev a number of scientific seminars, which served as a starting point for studies in optimization theory, modeling of production processes, and computer-aided design of complex objects. Glushkov was apparently among the first cyberneticists who called attention to the need for the development of methods of system analysis, whose application in conjunction with modern computers to the study of complex processes in economics, medicine, engineering, and military science might achieve the desired goals. At that time, Mikhalevich himself, as well as his students and followers, were beginning their systematic work in this field. Their work was typically motivated by practical needs, and therefore immediately found wide applications for the solution of real-life problems.The studies reviewed in this article can be classified into three main groups: a) development and application of numerical optimization methods; b) informatization of society and issues of economic cybernetics; c) development of multiprocessor computers and computer software.

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A decomposition approach to the solution of some integer programming problems with inexact data

Cited by 2 publications

References 4 publications

Methods of searching for guaranteeing and optimistic solutions to integer optimization problems under uncertainty

Methods of searching for guaranteeing and optimistic solutions to integer optimization problems under uncertainty

Some directions and results of research in mathematical programming and system analysis

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