Numerical Nonsmooth Optimization

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Numerical Nonsmooth Optimization

Author : Adil M. Bagirov
Publisher : Springer Nature
ISBN 13 : 3030349101
Total Pages : 696 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Numerical Nonsmooth Optimization by : Adil M. Bagirov

Download or read book Numerical Nonsmooth Optimization written by Adil M. Bagirov and published by Springer Nature. This book was released on 2020-02-28 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem’s special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. Given its scope, the book is ideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints

Author : Jiri Outrata
Publisher : Springer Science & Business Media
ISBN 13 : 1475728255
Total Pages : 281 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Nonsmooth Approach to Optimization Problems with Equilibrium Constraints by : Jiri Outrata

Download or read book Nonsmooth Approach to Optimization Problems with Equilibrium Constraints written by Jiri Outrata and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term "generalized bi level programming problems" was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective.

Nonsmooth/Nonconvex Mechanics

Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 1461302757
Total Pages : 505 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonsmooth/Nonconvex Mechanics by : David Yang Gao

Download or read book Nonsmooth/Nonconvex Mechanics written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.

Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control

Author : Marko M Makela
Publisher : World Scientific
ISBN 13 : 9814522414
Total Pages : 268 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control by : Marko M Makela

Download or read book Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control written by Marko M Makela and published by World Scientific. This book was released on 1992-05-07 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.

Numerical Optimization

Author : Joseph-Frédéric Bonnans
Publisher : Springer Science & Business Media
ISBN 13 : 3662050781
Total Pages : 421 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Numerical Optimization by : Joseph-Frédéric Bonnans

Download or read book Numerical Optimization written by Joseph-Frédéric Bonnans and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.

Introduction to Nonsmooth Optimization

Author : Adil Bagirov
Publisher : Springer
ISBN 13 : 3319081144
Total Pages : 372 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Introduction to Nonsmooth Optimization by : Adil Bagirov

Download or read book Introduction to Nonsmooth Optimization written by Adil Bagirov and published by Springer. This book was released on 2014-08-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

Numerical PDE-Constrained Optimization

Author : Juan Carlos De los Reyes
Publisher : Springer
ISBN 13 : 3319133950
Total Pages : 123 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Numerical PDE-Constrained Optimization by : Juan Carlos De los Reyes

Download or read book Numerical PDE-Constrained Optimization written by Juan Carlos De los Reyes and published by Springer. This book was released on 2015-02-06 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

Author : F. Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 0306480263
Total Pages : 304 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models by : F. Giannessi

Download or read book Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

Author : Qamrul Hasan Ansari
Publisher : CRC Press
ISBN 13 : 1439868212
Total Pages : 280 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization by : Qamrul Hasan Ansari

Download or read book Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization written by Qamrul Hasan Ansari and published by CRC Press. This book was released on 2013-07-18 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction. The first part of the book focuses on generalized convexity and generalized monotonicity. The authors investigate convexity and generalized convexity for both the differentiable and nondifferentiable case. For the nondifferentiable case, they introduce the concepts in terms of a bifunction and the Clarke subdifferential. The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings. The book discusses existence and uniqueness criteria for a variational inequality, the gap function associated with it, and numerical methods to solve it. It also examines characterizations of a solution set of an optimization problem and explores variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential. Integrating results on convexity, monotonicity, and variational inequalities into one unified source, this book deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The book shows how variational inequality theory not only serves as a tool for formulating a variety of equilibrium problems, but also provides algorithms for computational purposes.

Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov

Author : Napsu Karmitsa
Publisher : MDPI
ISBN 13 : 3039438352
Total Pages : 116 pages
Book Rating : 4.0/5 (394 download)

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Book Synopsis Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov by : Napsu Karmitsa

Download or read book Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov written by Napsu Karmitsa and published by MDPI. This book was released on 2020-12-18 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book was to collect the most recent methods developed for NSO and its practical applications. The book contains seven papers: The first is the foreword by the Guest Editors giving a brief review of NSO and its real-life applications and acknowledging the outstanding contributions of Professor Adil Bagirov to both the theoretical and practical aspects of NSO. The second paper introduces a new and very efficient algorithm for solving uncertain unit-commitment (UC) problems. The third paper proposes a new nonsmooth version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems. In the fourth paper, the abs-linear representation of piecewise linear functions is extended to yield simultaneously their DC decomposition as well as the pair of generalized gradients. The fifth paper presents the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and nonsmooth optimization problems in many practical applications. In the sixth paper, a problem concerning the scheduling of nuclear waste disposal is modeled as a nonsmooth multiobjective mixed-integer nonlinear optimization problem, and a novel method using the two-slope parameterized achievement scalarizing functions is introduced. Finally, the last paper considers binary classification of a multiple instance learning problem and formulates the learning problem as a nonconvex nonsmooth unconstrained optimization problem with a DC objective function.

Nonsmooth Equations in Optimization

Author : Diethard Klatte
Publisher : Springer Science & Business Media
ISBN 13 : 0306476169
Total Pages : 333 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Nonsmooth Equations in Optimization by : Diethard Klatte

Download or read book Nonsmooth Equations in Optimization written by Diethard Klatte and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.

Numerical Optimization

Author : Jorge Nocedal
Publisher : Springer Science & Business Media
ISBN 13 : 0387400656
Total Pages : 664 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Numerical Optimization by : Jorge Nocedal

Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Numerical Analysis and Optimization

Author : Mehiddin Al-Baali
Publisher : Springer Nature
ISBN 13 : 3030720403
Total Pages : 307 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Numerical Analysis and Optimization by : Mehiddin Al-Baali

Download or read book Numerical Analysis and Optimization written by Mehiddin Al-Baali and published by Springer Nature. This book was released on 2021-12-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020. Each chapter reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry. Many real-world, complex problems can be formulated as optimization tasks, and can be characterized further as large scale, unconstrained, constrained, non-convex, nondifferentiable or discontinuous, and therefore require adequate computational methods, algorithms and software tools. These same tools are often employed by researchers working in current IT hot topics, such as big data, optimization and other complex numerical algorithms in the cloud, devising special techniques for supercomputing systems. This interdisciplinary view permeates the work included in this volume. The NAO conference series is held every three years at Sultan Qaboos University, with the aim of bringing together a group of international experts and presenting novel and advanced applications to facilitate interdisciplinary studies among pure scientific and applied knowledge. It is a venue where prominent scientists gather to share innovative ideas and know-how relating to new scientific methodologies, to promote scientific exchange, to discuss possible future cooperations, and to promote the mobility of local and young researchers.

Nonconvex Optimization in Mechanics

Author : E.S. Mistakidis
Publisher : Springer Science & Business Media
ISBN 13 : 1461558298
Total Pages : 295 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Nonconvex Optimization in Mechanics by : E.S. Mistakidis

Download or read book Nonconvex Optimization in Mechanics written by E.S. Mistakidis and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonconvexity and nonsmoothness arise in a large class of engineering applica tions. In many cases of practical importance the possibilities offered by opti mization with its algorithms and heuristics can substantially improve the per formance and the range of applicability of classical computational mechanics algorithms. For a class of problems this approach is the only one that really works. The present book presents in a comprehensive way the application of opti mization algorithms and heuristics in smooth and nonsmooth mechanics. The necessity of this approach is presented to the reader through simple, represen tative examples. As things become more complex, the necessary material from convex and nonconvex optimization and from mechanics are introduced in a self-contained way. Unilateral contact and friction problems, adhesive contact and delamination problems, nonconvex elastoplasticity, fractal friction laws, frames with semi rigid connections, are among the applications which are treated in details here. Working algorithms are given for each application and are demonstrated by means of representative examples. The interested reader will find helpful references to up-to-date scientific and technical literature so that to be able to work on research or engineering topics which are not directly covered here.

Nonsmooth Optimization and Its Applications

Author : Seyedehsomayeh Hosseini
Publisher : Birkhäuser
ISBN 13 : 9783030113698
Total Pages : 149 pages
Book Rating : 4.1/5 (136 download)

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Book Synopsis Nonsmooth Optimization and Its Applications by : Seyedehsomayeh Hosseini

Download or read book Nonsmooth Optimization and Its Applications written by Seyedehsomayeh Hosseini and published by Birkhäuser. This book was released on 2019-04-16 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since nonsmooth optimization problems arise in a diverse range of real-world applications, the potential impact of efficient methods for solving such problems is undeniable. Even solving difficult smooth problems sometimes requires the use of nonsmooth optimization methods, in order to either reduce the problem’s scale or simplify its structure. Accordingly, the field of nonsmooth optimization is an important area of mathematical programming that is based on by now classical concepts of variational analysis and generalized derivatives, and has developed a rich and sophisticated set of mathematical tools at the intersection of theory and practice. This volume of ISNM is an outcome of the workshop "Nonsmooth Optimization and its Applications," which was held from May 15 to 19, 2017 at the Hausdorff Center for Mathematics, University of Bonn. The six research articles gathered here focus on recent results that highlight different aspects of nonsmooth and variational analysis, optimization methods, their convergence theory and applications.

Nonsmooth Optimization

Author : Claude Lemarechal
Publisher : Elsevier
ISBN 13 : 1483188760
Total Pages : 194 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Nonsmooth Optimization by : Claude Lemarechal

Download or read book Nonsmooth Optimization written by Claude Lemarechal and published by Elsevier. This book was released on 2014-05-19 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth Optimization contains the proceedings of a workshop on non-smooth optimization (NSO) held from March 28 to April 8,1977 in Austria under the auspices of the International Institute for Applied Systems Analysis. The papers explore the techniques and theory of NSO and cover topics ranging from systems of inequalities to smooth approximation of non-smooth functions, as well as quadratic programming and line searches. Comprised of nine chapters, this volume begins with a survey of Soviet research on subgradient optimization carried out since 1962, followed by a discussion on rates of convergence in subgradient optimization. The reader is then introduced to the method of subgradient optimization in an abstract setting and the minimal hypotheses required to ensure convergence; NSO and nonlinear programming; and bundle methods in NSO. A feasible descent algorithm for linearly constrained least squares problems is described. The book also considers sufficient minimization of piecewise-linear univariate functions before concluding with a description of the method of parametric decomposition in mathematical programming. This monograph will be of interest to mathematicians and mathematics students.

Modern Nonconvex Nondifferentiable Optimization

Author : Ying Cui
Publisher : SIAM
ISBN 13 : 161197674X
Total Pages : 792 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Modern Nonconvex Nondifferentiable Optimization by : Ying Cui

Download or read book Modern Nonconvex Nondifferentiable Optimization written by Ying Cui and published by SIAM. This book was released on 2021-12-02 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the fundamentals of classical smooth optimization and building on established convex programming techniques, this research monograph presents a foundation and methodology for modern nonconvex nondifferentiable optimization. It provides readers with theory, methods, and applications of nonconvex and nondifferentiable optimization in statistical estimation, operations research, machine learning, and decision making. A comprehensive and rigorous treatment of this emergent mathematical topic is urgently needed in today’s complex world of big data and machine learning. This book takes a thorough approach to the subject and includes examples and exercises to enrich the main themes, making it suitable for classroom instruction. Modern Nonconvex Nondifferentiable Optimization is intended for applied and computational mathematicians, optimizers, operations researchers, statisticians, computer scientists, engineers, economists, and machine learners. It could be used in advanced courses on optimization/operations research and nonconvex and nonsmooth optimization.