Convex Analysis And Minimization Algorithms I

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Author: Jean-Baptiste Hiriart-Urruty
Publisher: Springer
ISBN: 9783642081613
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Convex Analysis And Minimization Algorithms I by Jean-Baptiste Hiriart-Urruty


Original Title: Convex Analysis And Minimization Algorithms I

Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

Mathematical Tapas

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Author: Jean-Baptiste Hiriart-Urruty
Publisher: Springer
ISBN: 3319421867
Size: 26.24 MB
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Mathematical Tapas by Jean-Baptiste Hiriart-Urruty


Original Title: Mathematical Tapas

This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.

Inequality Problems In Mechanics And Applications

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Author: P.D. Panagiotopoulos
Publisher: Springer Science & Business Media
ISBN: 1461251524
Size: 39.40 MB
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Inequality Problems In Mechanics And Applications by P.D. Panagiotopoulos


Original Title: Inequality Problems In Mechanics And Applications

In a remarkably short time, the field of inequality problems has seen considerable development in mathematics and theoretical mechanics. Applied mechanics and the engineering sciences have also benefitted from these developments in that open problems have been treated and entirely new classes of problems have been formulated and solved. This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan. The book is intended for a variety of readers, mathematicians and engineers alike, as is detailed in the Guidelines for the Reader. It goes without saying that the work of G. Fichera, J. L. Lions, G. Maier, J. J. Moreau in originating and developing the theory of inequality problems has considerably influenced the present book. I also wish to acknowledge the helpful comments received from C. Bisbos, J. Haslinger, B. Kawohl, H. Matthies, H. O. May, D. Talaslidis and B. Werner. Credit is also due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally diligent work in the preparation of the fmal figures. Many thanks are also due to T. Finnegan and J. Gateley for their friendly assistance from the linguistic standpoint. I would also like to thank my editors in Birkhiiuser Verlag for their cooperation, and all those who helped in the preparation of the manuscript.

Convex Analysis And Minimization Algorithms Ii

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Author: Jean-Baptiste Hiriart-Urruty
Publisher: Springer Science & Business Media
ISBN: 366206409X
Size: 48.10 MB
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Convex Analysis And Minimization Algorithms Ii by Jean-Baptiste Hiriart-Urruty


Original Title: Convex Analysis And Minimization Algorithms Ii

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

Optimization On Low Rank Nonconvex Structures

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Author: Hiroshi Konno
Publisher: Springer Science & Business Media
ISBN: 1461540984
Size: 44.43 MB
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Optimization On Low Rank Nonconvex Structures by Hiroshi Konno


Original Title: Optimization On Low Rank Nonconvex Structures

Global optimization is one of the fastest developing fields in mathematical optimization. In fact, an increasing number of remarkably efficient deterministic algorithms have been proposed in the last ten years for solving several classes of large scale specially structured problems encountered in such areas as chemical engineering, financial engineering, location and network optimization, production and inventory control, engineering design, computational geometry, and multi-objective and multi-level optimization. These new developments motivated the authors to write a new book devoted to global optimization problems with special structures. Most of these problems, though highly nonconvex, can be characterized by the property that they reduce to convex minimization problems when some of the variables are fixed. A number of recently developed algorithms have been proved surprisingly efficient for handling typical classes of problems exhibiting such structures, namely low rank nonconvex structures. Audience: The book will serve as a fundamental reference book for all those who are interested in mathematical optimization.

Mathematical Analysis And Applications

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Author: V. Rădulescu
Publisher: Amer Inst of Physics
ISBN: 9780735403284
Size: 18.15 MB
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Mathematical Analysis And Applications by V. Rădulescu


Original Title: Mathematical Analysis And Applications

In these proceedings from the conference in September 2005, participants describe their work at the interface between mathematical physics, numerical analysis, optimal control and calculus of variations. Papers include work in nonlinear analysis and partial differential equations as well as classical mathematical analysis and dynamical systems. Ind

Linear And Nonlinear Functional Analysis With Applications

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Author: Philippe G. Ciarlet
Publisher: SIAM
ISBN: 1611972582
Size: 67.75 MB
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Linear And Nonlinear Functional Analysis With Applications by Philippe G. Ciarlet


Original Title: Linear And Nonlinear Functional Analysis With Applications

This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.

Mathematical Modeling And Optimization Of Complex Structures

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Author: Pekka Neittaanmäki
Publisher: Springer
ISBN: 3319235648
Size: 23.54 MB
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Mathematical Modeling And Optimization Of Complex Structures by Pekka Neittaanmäki


Original Title: Mathematical Modeling And Optimization Of Complex Structures

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.

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