Probability-theoretical generalization of the second lyapunov method

Nakonechnyi, A. N.

doi:10.1007/bf01130089

Cited by 2 publications

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“…Stochastic quasigradient methods for solving general optimization problems with nondifferentiable and nonconvex functions were developed in [32,57,58,[107][108][109][110][111][112][113][114][115][116][117] 9 The application of these methods in problems with nondifferentiable functions is highly relevant for important applied problems in which the modeled system is characterized by fast and unpredictable behavior. Stochastic quasigradient methods may be viewed as a generalization of stochastic approximation methods to constrained problems, and also as further development of random search methods.…”

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 99%

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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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Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 99%

“…Some versions of the stochastic quasigradient method with adaptive parameter control have been constructed and studied [114]. The asymptotic properties of iterative stochastic quasigradient methods (limit theorems, rate of convergence) have been studied in [116,117].…”

Section: Here S(c X) ~ II (C X) C P(c X) C Xmentioning

confidence: 99%