Nonlinear Programming 2
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Nonlinear Programming 2
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Author : O. L. Mangasarian
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Nonlinear Programming 2 written by O. L. Mangasarian and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Nonlinear Programming 2 covers the proceedings of the Special Interest Group on Mathematical Programming Symposium conducted by the Computer Sciences Department at the University of Wisconsin, Madison, on April 15-17, 1974. This book is divided into 13 chapters and begins with a survey of the global and superlinear convergence of a class of algorithms obtained by imposing changing bounds on the variables of the problem. The succeeding chapters deal with the convergence of the well-known reduced gradient method under suitable conditions and a superlinearly convergent quasi-Newton method for unconstrained minimization. These topics are followed by discussion of a superlinearly convergent algorithm for linearly constrained optimization problems and the effective methods for constrained optimization, namely the method of augmented Lagrangians. Other chapters explore a method for handling minimization problems with discontinuous derivatives and the advantages of factorizations of updating for Jacobian-related matrices in minimization problems. The last chapters present the Newton-like methods for the solution of nonlinear equations and inequalities, along with the various aspects of integer programming. This book will prove useful to mathematicians and computer scientists.
Nonlinear Programming
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Author : Peter Zörnig
language : en
Publisher: Walter de Gruyter
Release Date : 2014-01-31
Nonlinear Programming written by Peter Zörnig and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with Mathematics categories.
This book is an introduction to nonlinear programming. It deals with the theoretical foundations and solution methods, beginning with the classical procedures and reaching up to “modern” methods like trust region methods or procedures for nonlinear and global optimization. A comprehensive bibliography including diverse web sites with information about nonlinear programming, in particular software, is presented. Without sacrificing the necessary mathematical rigor, excessive formalisms are avoided. Several examples, exercises with detailed solutions, and applications are provided, making the text adequate for individual studies. The book is written for students from the fields of applied mathematics, engineering, economy, and computation.
Nonlinear Programming 2 Proceedings
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Author : Olvi L. Mangasarian
language : en
Publisher:
Release Date : 1975
Nonlinear Programming 2 Proceedings written by Olvi L. Mangasarian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Nonlinear Programming
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Author : Richard Cottle
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
Nonlinear Programming written by Richard Cottle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Control Applications Of Nonlinear Programming And Optimization
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Author : G. Di Pillo
language : en
Publisher: Elsevier
Release Date : 2014-05-17
Control Applications Of Nonlinear Programming And Optimization written by G. Di Pillo and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-17 with Technology & Engineering categories.
Control Applications of Nonlinear Programming and Optimization presents the proceedings of the Fifth IFAC Workshop held in Capri, Italy on June 11-14, 1985. The book covers various aspects of the optimization of control systems and of the numerical solution of optimization problems. The text also discusses specific applications concerned with the optimization of aircraft trajectories, of mineral and metallurgical processes, of wind tunnels, and of nuclear reactors. The book also considers computer-aided design of control systems. The book is useful to mathematicians, engineers, and computer engineers.
Nonlinear Programming 3
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Author : Olvi L. Mangasarian
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Nonlinear Programming 3 written by Olvi L. Mangasarian and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Nonlinear Programming 3 covers the proceedings of the Special Interest Group on Mathematical Programming Symposium conducted by the Computer Sciences Department at the University of Wisconsin, Madison, on July 11-13, 1977. This book is composed of 17 chapters. The first eight chapters describe some of the most effective methods available for solving linearly and nonlinearly constrained optimization problems. The subsequent chapter gives algorithms for the solution of nonlinear equations together with computational experience. Other chapters provide some applications of optimization in operations research and a measurement procedure for optimization algorithm efficiency. These topics are followed by discussion of the methods for solving large quadratic programs and algorithms for solving stationary and fixed point problems. The last chapters consider the minimization of certain types of nondifferentiable functions and a type of Newton method. This book will prove useful to mathematicians and computer scientists.
Nonlinear Optimization
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Author : H. A. Eiselt
language : en
Publisher: Springer Nature
Release Date : 2019-11-09
Nonlinear Optimization written by H. A. Eiselt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-09 with Mathematics categories.
This book provides a comprehensive introduction to nonlinear programming, featuring a broad range of applications and solution methods in the field of continuous optimization. It begins with a summary of classical results on unconstrained optimization, followed by a wealth of applications from a diverse mix of fields, e.g. location analysis, traffic planning, and water quality management, to name but a few. In turn, the book presents a formal description of optimality conditions, followed by an in-depth discussion of the main solution techniques. Each method is formally described, and then fully solved using a numerical example.
Optimization Of Biomass To Liquid Plant Setups And Capacity Using Nonlinear Programming
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Author : Lars-Peter Lauven
language : en
Publisher: Cuvillier Verlag
Release Date : 2011-10-12
Optimization Of Biomass To Liquid Plant Setups And Capacity Using Nonlinear Programming written by Lars-Peter Lauven and has been published by Cuvillier Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-12 with Business & Economics categories.
Potentially rising oil prices caused by an increasing relative scarcity of mineral oil have farreaching consequences for the transportation sector, the chemical industry and mineral oil companies in particular. As national laws in Germany require biofuels to be mixed into conventional fuel to an increasing extend (BioKraftQuG 2009), mineral oil companies need to identify economically competitive as well as technically feasible biofuel production processes to meet these requirements. A first generation of biofuels was introduced on a large scale but has been criticized for competing with the agricultural production of food and for yielding relatively modest quantities of fuel per hectare of agricultural land. For this reason, 2nd generation biofuel production pathways such as Biomass-to-Liquid (BtL), which convert lignocellulosic material into liquid hydrocarbons using Fischer-Tropsch synthesis, have been developed. While 2nd generation biofuels are superior to their 1st generation counterparts from a yield-per-hectare-perspective and cause less competition for agricultural soils, a significant disadvantage is the considerable investment required for the construction of Biomass-to-Liquid plants. The corresponding investment-related costs affect the competitiveness of 2nd generation biofuels negatively, leaving it in doubt whether BtL fuels could become an economically viable option. A frequently discussed way to improve specific investment-related costs is to increase plant sizes to improve economies of scale. While this improvement has been realized in several conventional kinds of plants like mineral oil refineries, power plants and Coal-to-Liquid plants, the application on BtL plants is complicated by the fact that larger plants are associated with higher specific biomass transportation costs. This is because a higher biomass input requires biomass to be transported over larger distances. The unresolved antagonism between economies of scale and specific biomass transportation costs has so far hindered the realization of BtL plants. The aim of this thesis is to develop a methodology to determine optimal BtL plant sizes by taking nonlinear factors into account. The methodology is required to determine a compromise between minimizing investment-related costs by applying economies of scale and minimizing specific biomass transportation costs by keeping the required transportation distances short. The optimal plant size is however influenced by a third influencing factor. Whether it is advantageous to transport biomass over a certain distance also depends on the value of a plant’s products. Biomass-to-Liquid plants can have a variety of product compositions depending on the catalyst and reaction temperature used in the biofuel synthesis reaction. Depending on which substances are produced and which are upgraded for sale, converted into fuels or combusted for electricity generation, both the value of the products and the required investment may differ considerably. While a number of processes, including biomass treatment and gasification, as well as the Fischer-Tropsch synthesis itself, are required for all considered plant setup alternatives, the choice of upgrading equipment may result in very dissimilar plant setups. By making the capacities of the individual upgrading processes the variables of the optimization model, economies of scale, specific biomass transportation costs and the products’ value are considered simultaneously for the first time. The thesis primarily focuses on the implementation of an optimization model and its application on a variety of scenarios. These scenarios are intended to represent different plant setups and logistics concepts. In order to assess the scale of differences in profitability, the essential influencing factors determining the profitability of BtL plants were included into the model calculations. As the problem at hand is neither linear nor quadratic, it cannot be solved reliably using established solvers for these two classes of problems. Instead, several solvers designed to handle non-quadratic nonlinear multidimensional problems were applied to find the most suitable way to approach the solution of the problem. The objective function has been designed to maximize the annual profit resulting from plant construction and operation. Maximizing this annual profit is subject to a number of primarily technical constraints. These result from the mass balances of the plant, its electricity demand and the specific requirements of individual processes. In addition to securing the validity of the mass balances, these constraints also ensure that the entire Fischer-Tropsch product stream undergoes some kind of upgrading, separation or combustion treatment. The sum of all processes producing salable products is used to approximate the required capacity of the plant as a whole. The total plant capacity then serves to calculate the investment required for the other plant processes and the costs for the purchase and transportation of the required input biomass. Biomass transportation distances are approximated by the radius of an assumed circular area from which biomass is supplied to the plant. Using cost functions that divide transportation costs into fixed and variable parts makes it possible to approximate the effect of rising specific biomass transportation costs in case of increasing plant capacities. The investigated scenario calculations suggest that under the assumed circumstances, fuel oriented low-temperature Fischer-Tropsch-based BtL plants are relatively competitive as long as the tax exemptions in Germany are maintained, but become significantly less attractive without them. By contrast, the combined production of both fuels and chemicals using hightemperature Fischer-Tropsch synthesis appears to be a more promising alternative, as chemicals are expected to earn a higher income in scenarios without tax exemptions. A third option, the production of Substitute Natural Gas, appears to be relatively uncompetitive unless methane prices rise significantly. In addition to comparing the economic attractiveness of different potential product distributions, a number of concepts have been investigated which are intended to improve Biomass-to-Liquid economics. Decentralized pretreatment of biomass, e.g. through fastpyrolysis, leads to larger optimal plant capacities, but the additional investment for the pretreatment units appears to overcompensate the improved economies of scale. By contrast, the combined use of train and road transportation was not assumed to be associated with additional investments. If train transportation is indeed feasible for a given plant location and specific biomass transportation costs are lower than for road transportation, combined traffic concepts should be used whenever possible. The construction of BtL plants in conjunction with mineral oil refineries is a way to reduce investment-related costs instead of transportation costs. While the resulting savings are significant for small BtL plants, they diminish if larger plant sizes are investigated. Cogasification of biomass with another input material is another way to reduce the costly transportation of biomass over large distances. Unless technical requirements significantly increase the cost of the gasification equipment, co-gasification concepts can improve the plant’s profitability even at relatively low quantities of a second fuel. The choice of fuels is however restricted by the Renewable Energy Directive that needs to be abided by in order to ensure the eligibility for tax exemptions. In case of lignite and hard coal, fossil CO2 emissions further complicate the application of co-gasification, as Renewable Energy Directive also limits the amount of fossil CO2 that biofuel production is allowed to cause. As savings caused by such concepts depend on the relative inefficiency of the concept that they are applied on, the effect of the implementation of several improvements diminishes if these address the same cost item. In this work, the nonlinear effects of economies of scale and biomass transportation costs for increasing Biomass-to-Liquid plant capacities has been modeled on a product-upgradingprocess basis for the first time. Potential investors and plant operators of Biomass-to-Liquid plants are thus enabled to determine both the optimal plant size and the most promising choice of products in order to maximize the prospective competitiveness of the plant.
Nonlinear Programming
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Author : Mordecai Avriel
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
Nonlinear Programming written by Mordecai Avriel and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
This overview provides a single-volume treatment of key algorithms and theories. Begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs, and then explores techniques for numerical solutions and unconstrained optimization methods. 1976 edition. Includes 58 figures and 7 tables.
Nondifferentiable And Two Level Mathematical Programming
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Author : Kiyotaka Shimizu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nondifferentiable And Two Level Mathematical Programming written by Kiyotaka Shimizu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.