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Quasiconvex Optimization and Location Theory

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 261/5 ( reviews)

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Book Synopsis Quasiconvex Optimization and Location Theory by : J.A. dos Santos Gromicho

Download or read book Quasiconvex Optimization and Location Theory written by J.A. dos Santos Gromicho. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional pro grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field C programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. [104]), Sniedovich shows how the study of such com positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. [9]) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. [16]). The distinction between global optimization problems (Ref. [54]) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.

Quasiconvex Optimization and Location Theory

1995 Convex functions
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Release : 1995
Genre : Convex functions
Kind : eBook
Book Rating : 214/5 ( reviews)

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Book Synopsis Quasiconvex Optimization and Location Theory by : Joaquim A. dos Gromicho

Download or read book Quasiconvex Optimization and Location Theory written by Joaquim A. dos Gromicho. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Flow Control in Manufacturing Systems

1998-08-31 Technology & Engineering
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Release : 1998-08-31
Genre : Technology & Engineering
Kind : eBook
Book Rating : 061/5 ( reviews)

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Book Synopsis Optimal Flow Control in Manufacturing Systems by : O. Maimon

Download or read book Optimal Flow Control in Manufacturing Systems written by O. Maimon. This book was released on 1998-08-31. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified optimal control approach to a large class of problems arising in the field of production planning and scheduling. It introduces a leading optimal flow control paradigm which results in efficient solutions for planning and scheduling problems. This book also introduces the reader to analytical and numerical methods of the maximum principle, used here as a mathematical instrument in modeling and solving production planning and scheduling problems. The book examines control of production flows rather than sequencing of distinct jobs. Methodologically, this paradigm allows us to progress from initial assumptions about a manufacturing environment, through mathematical models and construction of numerical methods, up to practical applications which prove the relevance of the theory developed here to the real world. Given a manufacturing system, the goal is to control the production, subject to given constraints, in such a way that the demands are tracked as closely as possible. The book considers a wide variety of problems encountered in actual production planning and scheduling. Among the problems are production flow sequencing and timing, capacity expansion and deterioration, subcontracting and overtime. The last chapter is entirely devoted to applications of the theory to scheduling production flows in real-life manufacturing systems. The enclosed disk provides software implementations of the developed methods with easy, convenient user interface. We aimed this book at a student audience - final year undergraduates as weIl as master and Ph. D.

Nonlinear Programming and Variational Inequality Problems

2013-06-29 Mathematics
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Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 91X/5 ( reviews)

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Book Synopsis Nonlinear Programming and Variational Inequality Problems by : Michael Patriksson

Download or read book Nonlinear Programming and Variational Inequality Problems written by Michael Patriksson. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.

Stable Parametric Programming

2013-11-21 Business & Economics
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Release : 2013-11-21
Genre : Business & Economics
Kind : eBook
Book Rating : 117/5 ( reviews)

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Book Synopsis Stable Parametric Programming by : S. Zlobec

Download or read book Stable Parametric Programming written by S. Zlobec. This book was released on 2013-11-21. Available in PDF, EPUB and Kindle. Book excerpt: Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as `controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form. Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis.

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