Rigorous Global Search Continuous Problems

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Rigorous Global Search Continuous Problems

Author : R. Baker Kearfott
ISBN : 9781475724950
Genre : Mathematics
File Size : 76.14 MB
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This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.
Category: Mathematics

Encyclopedia Of Optimization

Author : Christodoulos A. Floudas
ISBN : 9780387747583
Genre : Mathematics
File Size : 27.93 MB
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The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Category: Mathematics

A Reformulation Linearization Technique For Solving Discrete And Continuous Nonconvex Problems

Author : Hanif D. Sherali
ISBN : 9781475743883
Genre : Mathematics
File Size : 38.74 MB
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This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.
Category: Mathematics

Convexification And Global Optimization In Continuous And Mixed Integer Nonlinear Programming

Author : Mohit Tawarmalani
ISBN : 1402010311
Genre : Business & Economics
File Size : 32.11 MB
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This book provides an insightful and comprehensive treatment of convexification and global optimization of continuous and mixed-integer nonlinear programs. Developed for students, researchers, and practitioners, the book covers theory, algorithms, software, and applications. This thought-provoking book: -develops a powerful and widely-applicable framework for constructing closed-form expressions of convex envelopes of nonlinear functions; -presents a systematic treatment of branch-and-bound, while providing acceleration mechanisms and enhancements; -unifies ideas at the interface between operations research and computer science, devising efficient algorithmic implementation for global optimization; offers students, modelers, and algorithm developers a rich collection of models, applications, and numerical examples; -elucidates through geometric interpretations the concepts discussed throughout the book; -shows how optimization theory can lead to breakthroughs in diverse application areas, including molecular design, process and product design, facility location, and supply chain design and operation; -demonstrates that the BARON software developed by the authors can solve global optimization problems heretofore considered intractable, in an entirely automated manner on a personal computer. Audience: This book will be of interest to researchers in operations research, management science, applied mathematics, computer science, computational chemistry, and all branches of engineering. In addition, the book can be used in graduate level courses in nonlinear optimization, integer programming, global optimization, convex analysis, applied mathematics, and engineering design.
Category: Business & Economics

Introduction To Interval Analysis

Author : Ramon E. Moore
ISBN : 9780898717716
Genre : Interval analysis (Mathematics)
File Size : 30.30 MB
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An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.
Category: Interval analysis (Mathematics)

Convex Analysis And Global Optimization

Author : Hoang Tuy
ISBN : 0792348184
Genre : Business & Economics
File Size : 79.26 MB
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Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.
Category: Business & Economics

Proceedings

Author :
ISBN : UOM:39015047948784
Genre : Computer vision
File Size : 50.21 MB
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Category: Computer vision

Ninth Ieee International Conference On Computer Vision

Author : IEEE Computer Society. Technical Committee on Pattern Analysis and Machine Intelligence
ISBN : 0769519504
Genre : Computers
File Size : 48.89 MB
Format : PDF
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ICCV 2003 includes 43 full papers covering the latest research and progress in all areas of vision. The proceedings tackles necessary topics such as image representation, compression and coding, image segmentation, object recognition, active vision, 2D and 3D vision, sensing, and texture, color, and motion analysis.
Category: Computers

Bit

Author :
ISBN : UOM:39015049103743
Genre : Electronic journals
File Size : 83.57 MB
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Category: Electronic journals

Ksu Economic And Business Review

Author : Kyōto Sangyō Daigaku. Keizai Keiei Gakkai
ISBN : UCLA:L0082457300
Genre : Economic history
File Size : 73.6 MB
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Category: Economic history

Mathematica Japonicae

Author :
ISBN : UOM:39015049322830
Genre : Mathematics
File Size : 52.3 MB
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Category: Mathematics

Mathematical Reviews

Author :
ISBN : UOM:39015069723800
Genre : Mathematics
File Size : 61.91 MB
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Category: Mathematics

Computational Differentiation

Author : M. Berz
ISBN : UOM:39015049289773
Genre : Differential calculus
File Size : 30.77 MB
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This volume goes beyond the first volume published in 1991 (SIAM) in that it encompasses both the automatic transformation of computer programs as well as the methodologies for the efficient exploitation of mathematical underpinnings or program structure.
Category: Differential calculus