Minimization Methods For Non Differentiable Functions
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Minimization Methods For Non Differentiable Functions
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Author : N.Z. Shor
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Minimization Methods For Non Differentiable Functions written by N.Z. Shor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In recent years much attention has been given to the development of auto matic systems of planning, design and control in various branches of the national economy. Quality of decisions is an issue which has come to the forefront, increasing the significance of optimization algorithms in math ematical software packages for al,ltomatic systems of various levels and pur poses. Methods for minimizing functions with discontinuous gradients are gaining in importance and the ~xperts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the con struction of efficient techniques for solving large scale problems. This monograph summarizes to a certain extent fifteen years of the author's work on developing generalized gradient methods for nonsmooth minimization. This work started in the department of economic cybernetics of the Institute of Cybernetics of the Ukrainian Academy of Sciences under the supervision of V.S. Mikhalevich, a member of the Ukrainian Academy of Sciences, in connection with the need for solutions to important, practical problems of optimal planning and design. In Chap. I we describe basic classes of nonsmooth functions that are dif ferentiable almost everywhere, and analyze various ways of defining generalized gradient sets. In Chap. 2 we study in detail various versions of the su bgradient method, show their relation to the methods of Fejer-type approximations and briefly present the fundamentals of e-subgradient methods.
Minimization Methods For Non Differentiable Functions
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Author : N. Z. Shor
language : en
Publisher:
Release Date : 1984-12-01
Minimization Methods For Non Differentiable Functions written by N. Z. Shor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-01 with categories.
Nondifferentiable Optimization And Polynomial Problems
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Author : N.Z. Shor
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Nondifferentiable Optimization And Polynomial Problems written by N.Z. Shor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.
Modern Nonconvex Nondifferentiable Optimization
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Author : Ying Cui
language : en
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Release Date : 2022
Modern Nonconvex Nondifferentiable Optimization written by Ying Cui and has been published by Society for Industrial and Applied Mathematics (SIAM) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Convex functions categories.
"This monograph serves present and future needs where nonconvexity and nondifferentiability are inevitably present in the faithful modeling of real-world applications of optimization"--
Computational Combinatorial Optimization
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Author : Michael Jünger
language : en
Publisher: Springer
Release Date : 2001-01-01
Computational Combinatorial Optimization written by Michael Jünger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality.
Numerical Methods For Differential Equations Optimization And Technological Problems
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Author : Sergey Repin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-13
Numerical Methods For Differential Equations Optimization And Technological Problems written by Sergey Repin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-13 with Technology & Engineering categories.
This book contains the results in numerical analysis and optimization presented at the ECCOMAS thematic conference “Computational Analysis and Optimization” (CAO 2011) held in Jyväskylä, Finland, June 9–11, 2011. Both the conference and this volume are dedicated to Professor Pekka Neittaanmäki on the occasion of his sixtieth birthday. It consists of five parts that are closely related to his scientific activities and interests: Numerical Methods for Nonlinear Problems; Reliable Methods for Computer Simulation; Analysis of Noised and Uncertain Data; Optimization Methods; Mathematical Models Generated by Modern Technological Problems. The book also includes a short biography of Professor Neittaanmäki.
Optimization And Applications
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Author : Yury Evtushenko
language : en
Publisher: Springer
Release Date : 2019-01-09
Optimization And Applications written by Yury Evtushenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-09 with Mathematics categories.
This book constitutes the refereed proceedings of the 9th International Conference on Optimization and Applications, OPTIMA 2018, held in Petrovac, Montenegro, in October 2018.The 35 revised full papers and the one short paper presented were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on mathematical programming; combinatorial and discrete optimization; optimal control; optimization in economy, finance and social sciences; applications.
Optimization Models
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Author : Giuseppe C. Calafiore
language : en
Publisher: Cambridge University Press
Release Date : 2014-10-31
Optimization Models written by Giuseppe C. Calafiore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-31 with Business & Economics categories.
This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects.
Computational Techniques And Applications Ctac 95 Proceedings Of The Seventh Biennial Conference
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Author : Robert L May
language : en
Publisher: World Scientific
Release Date : 1996-08-30
Computational Techniques And Applications Ctac 95 Proceedings Of The Seventh Biennial Conference written by Robert L May and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-30 with categories.
This proceedings contains seven invited papers and 100 contributed papers. The topics covered range from studies of theoretical aspects of computational methods through to simulations of large-scale industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Developers and users of computational techniques who wish to keep up with recent developments in the application of modern computational technology to problems in science and engineering will find much of interest in this volume.
Dynamic Modelling And Control Of National Economies 1989
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Author : N.M. Christodoulakis
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Dynamic Modelling And Control Of National Economies 1989 written by N.M. Christodoulakis and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Business & Economics categories.
The Symposium aimed at analysing and solving the various problems of representation and analysis of decision making in economic systems starting from the level of the individual firm and ending up with the complexities of international policy coordination. The papers are grouped into subject areas such as game theory, control methods, international policy coordination and the applications of artificial intelligence and experts systems as a framework in economic modelling and control. The Symposium therefore provides a wide range of important information for those involved or interested in the planning of company and national economics.