Download or read book Mixed Integer Nonlinear Programming written by Jon Lee and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.

Download or read book Nonlinear and Mixed Integer Optimization written by Christodoulos A. Floudas and published by Oxford University Press. This book was released on 1995-10-05 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the fundamentals of nonlinear and mixed-integer optimisation, and their applications in the important area of process synthesis in chemical engineering. Topics that are unique include the theory and methods for mixed-integer nonlinear optimisation, introduction to modelling issues in process synthesis, and optimisation-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems.

Download or read book Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming written by Ivo Nowak and published by Springer Science & Business Media. This book was released on 2005-08-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many ?elds, such as process industry, engineering design, communications, and ?nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di?cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: • A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. • In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. • The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.

Download or read book Integer Programming and Combinatorial Optimization written by Karen Aardal and published by Springer Nature. This book was released on 2022-05-27 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 23rd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2022, held in Eindhoven, The Netherlands, in June 2022. The 33 full papers presented were carefully reviewed and selected from 93 submissions addressing key techniques of document analysis. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting the latest results of theory and practice of the various aspects of discrete optimization.

Download or read book Disjunctive Programming written by Egon Balas and published by Springer. This book was released on 2018-11-27 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business.

Download or read book Integer Programming and Combinatorial Optimization written by Andrea Lodi and published by Springer. This book was released on 2008-05-24 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains the papers selected for presentation at IPCO 2008, the 13th International Conference on Integer Programming and Combinatorial - timization that was held in Bertinoro (Italy), May 26–28, 2008. The IPCO series of conferences, sponsored by the Mathematical Progr- ming Society, highlights recent developments in theory, computation, and app- cation of integer programming and combinatorial optimization. The ?rst conf- ence took place in 1990; starting from IPCO 1995, the proceedings are published in the Lecture Notes in Computer Science series. The 12 previous IPCO conferences were held in Waterloo (Canada) 1990, Pittsburgh (USA) 1992, Erice (Italy) 1993, Copenhagen (Denmark) 1995 [LNCS 920], Vancouver (Canada) 1996 [LNCS 1084], Houston (USA) 1998 [LNCS 1412], Graz (Austria) 1999 [LNCS 1610], Utrecht (The Netherlands) 2001 [LNCS 2081], Boston (USA) 2002 [LNCS 2337], New York (USA) 2004 [LNCS 2986], Berlin (Germany) 2005 [LNCS 3509], and Ithaca (USA) 2007 [LNCS 4168]. The c- ference is not held in the years when the International Symposium of the Ma- ematical Programming Society takes place.

Download or read book Integer Programming and Combinatorial Optimization written by Friedrich Eisenbrand and published by Springer Science & Business Media. This book was released on 2010-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2010, held in Lausanne, Switzerland in June 2010. The 34 papers presented were carefully reviewed and selected from 135 submissions. The conference has become the main forum for recent results in integer programming and combinatorial optimization in the non-symposium years.

Download or read book Tutorials in Operations Research written by Institute for Operations Research and the Management Sciences. National Meeting and published by INFORMS. This book was released on 2008 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large Scale Optimization with Applications written by Lorenz T. Biegler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.

Download or read book Foundations of Bilevel Programming written by Stephan Dempe and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful.

Download or read book Optimization and Anti optimization of Structures Under Uncertainty written by Isaac Elishakoff and published by World Scientific. This book was released on 2010 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume presents a collaboration between internationally recognized experts on anti-optimization and structural optimization, and summarizes various novel ideas, methodologies and results studied over 20 years. The book vividly demonstrates how the concept of uncertainty should be incorporated in a rigorous manner during the process of designing real-world structures. The necessity of anti-optimization approach is first demonstrated, then the anti-optimization techniques are applied to static, dynamic and buckling problems, thus covering the broadest possible set of applications. Finally, anti-optimization is fully utilized by a combination of structural optimization to produce the optimal design considering the worst-case scenario. This is currently the only book that covers the combination of optimization and anti-optimization. It shows how various optimization techniques are used in the novel anti-optimization technique, and how the structural optimization can be exponentially enhanced by incorporating the concept of worst-case scenario, thereby increasing the safety of the structures designed in various fields of engineering.

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 2410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Download or read book Applied Integer Programming written by Der-San Chen and published by John Wiley & Sons. This book was released on 2010-01-12 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems.

Download or read book Integer Programming and Related Areas written by C. Kastning and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integer Prograw~ing is one of the most fascinating and difficult areas in the field of Mathematical Optimization. Due to this fact notable research contributions to Integer Programming have been made in very different branches of mathematics and its applications. Since these publications are scattered over many journals, proceedings volumes, monographs, and working papers, a comprehensive bibliography of all these sources is a helpful tool even for specialists in this field. I initiated this compilation of literature in 1970 at the Institut fur ~konometrie und Operations Research, University of Bonn. Since then many collaborators have contributed to and worked on it. Among them Dipl.-Math. Claus Kastning has done the bulk of the work. With great perseverance and diligence he has gathered all the material and checked it with the original sources. The main aim was to incorporate rare and not easily accessible sources like Russian journals, preprints or unpublished papers. Without the invaluable and dedicated engagement of Claus Kastning the bibliography would never have reached this final version. For this reason he must be considered its responsible editor. As with any other collection this literature list has a subjective viewpoint and may be in some sense incomplete. We have however tried to be as complete as possible. The bibliography contains 4704 different publications by 6767 authors which were classified by 11839 descriptor entries.

Download or read book Optimization Methods Applied to Power Systems written by Francisco G. Montoya and published by MDPI. This book was released on 2021-03-16 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electrical power systems are complex networks that include a set of electrical components that allow distributing the electricity generated in the conventional and renewable power plants to distribution systems so it can be received by final consumers (businesses and homes). In practice, power system management requires solving different design, operation, and control problems. Bearing in mind that computers are used to solve these complex optimization problems, this book includes some recent contributions to this field that cover a large variety of problems. More specifically, the book includes contributions about topics such as controllers for the frequency response of microgrids, post-contingency overflow analysis, line overloads after line and generation contingences, power quality disturbances, earthing system touch voltages, security-constrained optimal power flow, voltage regulation planning, intermittent generation in power systems, location of partial discharge source in gas-insulated switchgear, electric vehicle charging stations, optimal power flow with photovoltaic generation, hydroelectric plant location selection, cold-thermal-electric integrated energy systems, high-efficiency resonant devices for microwave power generation, security-constrained unit commitment, and economic dispatch problems.

Download or read book Handbook of combinatorial optimization 1 written by Dingzhu Du and published by Springer Science & Business Media. This book was released on 1998 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of a multi-volume set, which deals with several algorithmic approaches for discrete problems as well as many combinatorial problems. It is addressed to researchers in discrete optimization, and to all scientists who use combinatorial optimization methods to model and solve problems.