Optimization Theory And Related Topics
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| Author | : Simeon Reich |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 296 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821869086 |
This volume contains the proceedings of the workshop on Optimization Theory and Related Topics, held in memory of Dan Butnariu, from January 11-14, 2010, in Haifa, Israel. An active researcher in various fields of applied mathematics, Butnariu published over 80 papers. His extensive bibliography is included in this volume. The articles in this volume cover many different areas of Optimization Theory and its applications: maximal monotone operators, sensitivity estimates via Lyapunov functions, inverse Newton transforms, infinite-horizon Pontryagin principles, singular optimal control problems with state delays, descent methods for mixed variational inequalities, games on MV-algebras, ergodic convergence in subgradient optimization, applications to economics and technology planning, the exact penalty property in constrained optimization, nonsmooth inverse problems, Bregman distances, retraction methods in Banach spaces, and iterative methods for solving equilibrium problems. This volume will be of interest to both graduate students and research mathematicians.
| Author | : L. Cesari |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 555 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461381657 |
This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.
| Author | : Hubertus Th. Jongen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 436 |
| Release | : 2007-05-08 |
| Genre | : Mathematics |
| ISBN | : 1402080999 |
This volume provides a comprehensive introduction to the theory of (deterministic) optimization. It covers both continuous and discrete optimization. This allows readers to study problems under different points-of-view, which supports a better understanding of the entire field. Many exercises are included to increase the reader's understanding.
| Author | : Donald A. Pierre |
| Publisher | : Courier Corporation |
| Total Pages | : 644 |
| Release | : 2012-07-12 |
| Genre | : Mathematics |
| ISBN | : 0486136957 |
Broad-spectrum approach to important topic. Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and linear programming, optimality and dynamic programming, more. 1969 edition.
| Author | : Wenyu Sun |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 689 |
| Release | : 2006-08-06 |
| Genre | : Mathematics |
| ISBN | : 0387249761 |
Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.
| Author | : Stephen P. Boyd |
| Publisher | : Cambridge University Press |
| Total Pages | : 744 |
| Release | : 2004-03-08 |
| Genre | : Business & Economics |
| ISBN | : 9780521833783 |
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
| Author | : Yun-Bin Zhao |
| Publisher | : CRC Press |
| Total Pages | : 222 |
| Release | : 2018-07-04 |
| Genre | : Business & Economics |
| ISBN | : 1351624148 |
Seeking sparse solutions of underdetermined linear systems is required in many areas of engineering and science such as signal and image processing. The efficient sparse representation becomes central in various big or high-dimensional data processing, yielding fruitful theoretical and realistic results in these fields. The mathematical optimization plays a fundamentally important role in the development of these results and acts as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and so on. This has attracted the interest of many researchers at the interface of engineering, mathematics and computer science. Sparse Optimization Theory and Methods presents the state of the art in theory and algorithms for signal recovery under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analysed in this book. Under the RSP assumption, the author also provides a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and the author’s latest research in the field that have not appeared in other books.
| Author | : Bernhard Korte |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 596 |
| Release | : 2006-01-27 |
| Genre | : Mathematics |
| ISBN | : 3540292977 |
This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.
| Author | : S. S. Rao |
| Publisher | : New Age International |
| Total Pages | : 936 |
| Release | : 2000 |
| Genre | : Engineering |
| ISBN | : 9788122411492 |
A Rigorous Mathematical Approach To Identifying A Set Of Design Alternatives And Selecting The Best Candidate From Within That Set, Engineering Optimization Was Developed As A Means Of Helping Engineers To Design Systems That Are Both More Efficient And Less Expensive And To Develop New Ways Of Improving The Performance Of Existing Systems.Thanks To The Breathtaking Growth In Computer Technology That Has Occurred Over The Past Decade, Optimization Techniques Can Now Be Used To Find Creative Solutions To Larger, More Complex Problems Than Ever Before. As A Consequence, Optimization Is Now Viewed As An Indispensable Tool Of The Trade For Engineers Working In Many Different Industries, Especially The Aerospace, Automotive, Chemical, Electrical, And Manufacturing Industries.In Engineering Optimization, Professor Singiresu S. Rao Provides An Application-Oriented Presentation Of The Full Array Of Classical And Newly Developed Optimization Techniques Now Being Used By Engineers In A Wide Range Of Industries. Essential Proofs And Explanations Of The Various Techniques Are Given In A Straightforward, User-Friendly Manner, And Each Method Is Copiously Illustrated With Real-World Examples That Demonstrate How To Maximize Desired Benefits While Minimizing Negative Aspects Of Project Design.Comprehensive, Authoritative, Up-To-Date, Engineering Optimization Provides In-Depth Coverage Of Linear And Nonlinear Programming, Dynamic Programming, Integer Programming, And Stochastic Programming Techniques As Well As Several Breakthrough Methods, Including Genetic Algorithms, Simulated Annealing, And Neural Network-Based And Fuzzy Optimization Techniques.Designed To Function Equally Well As Either A Professional Reference Or A Graduate-Level Text, Engineering Optimization Features Many Solved Problems Taken From Several Engineering Fields, As Well As Review Questions, Important Figures, And Helpful References.Engineering Optimization Is A Valuable Working Resource For Engineers Employed In Practically All Technological Industries. It Is Also A Superior Didactic Tool For Graduate Students Of Mechanical, Civil, Electrical, Chemical And Aerospace Engineering.
| Author | : Alexander M. Rubinov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 466 |
| Release | : 2013-04-17 |
| Genre | : Computers |
| ISBN | : 147576099X |
This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations Re search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both con tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Contributed paper, which contain new and interesting results, are also included. The fields of the presented papers are very large as demonstrated by the following selection of key words from selected papers in this volume: • optimal control, stochastic optimal control, MATLAB, economic models, implicit constraints, Bellman principle, Markov process, decision-making under uncertainty, risk aversion, dynamic programming, optimal value function. • emergent computation, complexity, traveling salesman problem, signal estimation, neural networks, time congestion, teletraffic. • gap functions, nonsmooth variational inequalities, derivative-free algo rithm, Newton's method. • auxiliary function, generalized penalty function, modified Lagrange func tion. • convexity, quasiconvexity, abstract convexity.
