A Reformulation Linearization Technique For Solving Discrete And Continuous Nonconvex Problems
Download A Reformulation Linearization Technique For Solving Discrete And Continuous Nonconvex Problems full books in PDF, epub, and Kindle. Read online free A Reformulation Linearization Technique For Solving Discrete And Continuous Nonconvex Problems ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Hanif D. Sherali |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 529 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475743882 |
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.
| Author | : Jon Lee |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 687 |
| Release | : 2011-12-02 |
| Genre | : Mathematics |
| ISBN | : 1461419271 |
Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.
| Author | : Ding-Zhu Du |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 2410 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461303036 |
Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).
| Author | : Stephan Dempe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 281 |
| Release | : 2006-09-19 |
| Genre | : Mathematics |
| ISBN | : 0387342214 |
This book focuses on the tremendous development that has taken place recently in the field of of nondifferentiable nonconvex optimization. Coverage includes the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the co-derivative of Mordukhovich), the opening of new applications (the calibration of water supply systems), and the elaboration of new solution algorithms (e.g., smoothing methods).
| Author | : Gilbert Laporte |
| Publisher | : Springer |
| Total Pages | : 650 |
| Release | : 2015-02-25 |
| Genre | : Business & Economics |
| ISBN | : 3319131117 |
This comprehensive and clearly structured book presents essential information on modern Location Science. The book is divided into three parts: basic concepts, advanced concepts and applications. Written by the most respected specialists in the field and thoroughly reviewed by the editors, it first lays out the fundamental problems in Location Science and provides the reader with basic background information on location theory. Part II covers advanced models and concepts, broadening and expanding on the content presented in Part I. It provides the reader with important tools to help them understand and solve real-world location problems. Part III is dedicated to linking Location Science with other areas like GIS, telecommunications, healthcare, rapid transit networks, districting problems and disaster events, presenting a wide range of applications. This part enables the reader to understand the role of facility location in such areas, as well as to learn how to handle realistic location problems. The book is intended for researchers working on theory and applications involving location problems and models. It is also suitable as a textbook for graduate courses on facility location.
| Author | : Jean Bernard Lasserre |
| Publisher | : Cambridge University Press |
| Total Pages | : 355 |
| Release | : 2015-02-19 |
| Genre | : Mathematics |
| ISBN | : 1316240398 |
This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.
| Author | : Kenneth H. Rosen |
| Publisher | : CRC Press |
| Total Pages | : 1612 |
| Release | : 2017-10-19 |
| Genre | : Mathematics |
| ISBN | : 1584887818 |
Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.
| Author | : R. Horst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 376 |
| Release | : 2000-12-31 |
| Genre | : Computers |
| ISBN | : 9780792367567 |
A textbook for an undergraduate course in mathematical programming for students with a knowledge of elementary real analysis, linear algebra, and classical linear programming (simple techniques). Focuses on the computation and characterization of global optima of nonlinear functions, rather than the locally optimal solutions addressed by most books on optimization. Incorporates the theoretical, algorithmic, and computational advances of the past three decades that help solve globally multi-extreme problems in the mathematical modeling of real world systems. Annotation copyright by Book News, Inc., Portland, OR
| Author | : Xiang-Sun Zhang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 2000-10-31 |
| Genre | : Business & Economics |
| ISBN | : 9780792365150 |
The book consists of three parts. The first part introduces concepts and algorithms in optimization theory, which have been used in neural network research. The second part covers main neural network models and their theoretical analysis. The third part of the book introduces various neural network models for solving nonlinear programming problems and combinatorial optimization problems. Audience: Graduate students and researchers who are interested in the intersection of optimization theory and artificial neural networks. The book is appropriate for graduate courses.
| Author | : Hubertus Th. Jongen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 516 |
| Release | : 2013-12-11 |
| Genre | : Mathematics |
| ISBN | : 1461500176 |
At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies. Roughly speaking, the topology of lower level sets only may change when passing a level which corresponds to a stationary point (or Karush-Kuhn Tucker point). We study elements of Morse Theory, both in the unconstrained and constrained case. Special attention is paid to the degree of differentiabil ity of the functions under consideration. The reader will become motivated to discuss the possible shapes and forms of functions that may possibly arise within a given problem framework. In a separate chapter we show how certain ideas may be carried over to nonsmooth items, such as problems of Chebyshev approximation type. We made this choice in order to show that a good under standing of regular smooth problems may lead to a straightforward treatment of "just" continuous problems by means of suitable perturbation techniques, taking a priori nonsmoothness into account. Moreover, we make a focal point analysis in order to emphasize the difference between inner product norms and, for example, the maximum norm. Then, specific tools from algebraic topol ogy, in particular homology theory, are treated in some detail. However, this development is carried out only as far as it is needed to understand the relation between critical points of a function on a manifold with structured boundary. Then, we pay attention to three important subjects in nonlinear optimization.
