Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control

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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.

Nonsmooth Optimization

Author : Marko M. Mäkelä
Publisher :
ISBN 13 : 9789516803077
Total Pages : 168 pages
Book Rating : 4.8/5 (3 download)

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Book Synopsis Nonsmooth Optimization by : Marko M. Mäkelä

Download or read book Nonsmooth Optimization written by Marko M. Mäkelä and published by . This book was released on 1990 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Methods of Dynamic and Nonsmooth Optimization

Author : Frank H. Clarke
Publisher : SIAM
ISBN 13 : 0898712416
Total Pages : 94 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Methods of Dynamic and Nonsmooth Optimization by : Frank H. Clarke

Download or read book Methods of Dynamic and Nonsmooth Optimization written by Frank H. Clarke and published by SIAM. This book was released on 1989-01-01 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the elements of a unified approach to optimization based on 'nonsmooth analysis', a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.

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.

Optimization and Control with Applications

Author : Liqun Qi
Publisher : Springer Science & Business Media
ISBN 13 : 0387242554
Total Pages : 587 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Optimization and Control with Applications by : Liqun Qi

Download or read book Optimization and Control with Applications written by Liqun Qi and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of 28 refereed papers grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. Suitable for researchers, practitioners and postgrads.

Optimization and Nonsmooth Analysis

Author : Frank H. Clarke
Publisher : SIAM
ISBN 13 : 0898712564
Total Pages : 317 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Optimization and Nonsmooth Analysis by : Frank H. Clarke

Download or read book Optimization and Nonsmooth Analysis written by Frank H. Clarke and published by SIAM. This book was released on 1990-01-01 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Reviews said of this book that it was 'destined to become a classical reference.' This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.

Nonsmooth Optimization and Its Applications

Author : Seyedehsomayeh Hosseini
Publisher : Springer
ISBN 13 : 3030113701
Total Pages : 149 pages
Book Rating : 4.0/5 (31 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 Springer. This book was released on 2019-03-29 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 Analysis and Geometric Methods in Deterministic Optimal Control

Author : Boris S. Mordukhovich
Publisher : Springer
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control by : Boris S. Mordukhovich

Download or read book Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control written by Boris S. Mordukhovich and published by Springer. This book was released on 1996-06-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz ing the workshop and editing the proceedings. We also take this oppor tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.

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.

Optimal Control Via Nonsmooth Analysis

Author : Philip Daniel Loewen
Publisher :
ISBN 13 : 9781470439163
Total Pages : 153 pages
Book Rating : 4.4/5 (391 download)

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Book Synopsis Optimal Control Via Nonsmooth Analysis by : Philip Daniel Loewen

Download or read book Optimal Control Via Nonsmooth Analysis written by Philip Daniel Loewen and published by . This book was released on 1993 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algorithms for Worst-Case Design and Applications to Risk Management

Author : Berç Rustem
Publisher : Princeton University Press
ISBN 13 : 1400825113
Total Pages : 405 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Algorithms for Worst-Case Design and Applications to Risk Management by : Berç Rustem

Download or read book Algorithms for Worst-Case Design and Applications to Risk Management written by Berç Rustem and published by Princeton University Press. This book was released on 2009-02-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recognizing that robust decision making is vital in risk management, this book provides concepts and algorithms for computing the best decision in view of the worst-case scenario. The main tool used is minimax, which ensures robust policies with guaranteed optimal performance that will improve further if the worst case is not realized. The applications considered are drawn from finance, but the design and algorithms presented are equally applicable to problems of economic policy, engineering design, and other areas of decision making. Critically, worst-case design addresses not only Armageddon-type uncertainty. Indeed, the determination of the worst case becomes nontrivial when faced with numerous--possibly infinite--and reasonably likely rival scenarios. Optimality does not depend on any single scenario but on all the scenarios under consideration. Worst-case optimal decisions provide guaranteed optimal performance for systems operating within the specified scenario range indicating the uncertainty. The noninferiority of minimax solutions--which also offer the possibility of multiple maxima--ensures this optimality. Worst-case design is not intended to necessarily replace expected value optimization when the underlying uncertainty is stochastic. However, wise decision making requires the justification of policies based on expected value optimization in view of the worst-case scenario. Conversely, the cost of the assured performance provided by robust worst-case decision making needs to be evaluated relative to optimal expected values. Written for postgraduate students and researchers engaged in optimization, engineering design, economics, and finance, this book will also be invaluable to practitioners in risk management.

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.

Optimal Control

Author : Richard Vinter
Publisher : Birkhäuser
ISBN 13 : 9780817649906
Total Pages : 500 pages
Book Rating : 4.6/5 (499 download)

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Book Synopsis Optimal Control by : Richard Vinter

Download or read book Optimal Control written by Richard Vinter and published by Birkhäuser. This book was released on 2010-07-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control." —Mathematical Reviews “Thanks to a great effort to be self-contained, [this book] renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis)." —Automatica

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.

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.

Mathematical Modeling and Optimization of Complex Structures

Author : Pekka Neittaanmäki
Publisher : Springer
ISBN 13 : 3319235648
Total Pages : 328 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Mathematical Modeling and Optimization of Complex Structures by : Pekka Neittaanmäki

Download or read book Mathematical Modeling and Optimization of Complex Structures written by Pekka Neittaanmäki and published by Springer. This book was released on 2015-10-07 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimization algorithms; * Optimal control problems with distributed and discrete control; * Shape optimization and shape design problems in science and engineering; * Sensitivity analysis and parameters optimization of complex systems.

Optimal Control

Author : William W. Hager
Publisher : Springer
ISBN 13 : 9781441947963
Total Pages : 516 pages
Book Rating : 4.9/5 (479 download)

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Book Synopsis Optimal Control by : William W. Hager

Download or read book Optimal Control written by William W. Hager and published by Springer. This book was released on 2010-12-09 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: February 27 - March 1, 1997, the conference Optimal Control: The ory, Algorithms, and Applications took place at the University of Florida, hosted by the Center for Applied Optimization. The conference brought together researchers from universities, industry, and government laborato ries in the United States, Germany, Italy, France, Canada, and Sweden. There were forty-five invited talks, including seven talks by students. The conference was sponsored by the National Science Foundation and endorsed by the SIAM Activity Group on Control and Systems Theory, the Mathe matical Programming Society, the International Federation for Information Processing (IFIP), and the International Association for Mathematics and Computers in Simulation (IMACS). Since its inception in the 1940s and 1950s, Optimal Control has been closely connected to industrial applications, starting with aerospace. The program for the Gainesville conference, which reflected the rich cross-disci plinary flavor of the field, included aerospace applications as well as both novel and emerging applications to superconductors, diffractive optics, non linear optics, structural analysis, bioreactors, corrosion detection, acoustic flow, process design in chemical engineering, hydroelectric power plants, sterilization of canned foods, robotics, and thermoelastic plates and shells. The three days of the conference were organized around the three confer ence themes, theory, algorithms, and applications. This book is a collection of the papers presented at the Gainesville conference. We would like to take this opportunity to thank the sponsors and participants of the conference, the authors, the referees, and the publisher for making this volume possible.