Mixed Integer Nonlinear Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mixed Integer Nonlinear Programming write by Jon Lee. This book was released on 2011-12-02. Mixed Integer Nonlinear Programming available in PDF, EPUB and Kindle. 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.
Nonlinear and Mixed-Integer Optimization
Nonlinear and Mixed-Integer Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear and Mixed-Integer Optimization write by Christodoulos A. Floudas. This book was released on 1995-10-05. Nonlinear and Mixed-Integer Optimization available in PDF, EPUB and Kindle. 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.
Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming write by Mohit Tawarmalani. This book was released on 2013-04-17. Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming available in PDF, EPUB and Kindle. Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.
Disjunctive Programming
Disjunctive Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Disjunctive Programming write by Egon Balas. This book was released on 2018-11-27. Disjunctive Programming available in PDF, EPUB and Kindle. 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.
Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming write by Ivo Nowak. This book was released on 2005-08-15. Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming available in PDF, EPUB and Kindle. 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.
