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| Author | : Monique Guignard-Spielberg |
| Publisher | : North Holland |
| Total Pages | : 262 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : M. Guignard |
| Publisher | : |
| Total Pages | : 240 |
| Release | : 1982 |
| Genre | : |
| ISBN | : |
| Author | : Fiacco |
| Publisher | : Academic Press |
| Total Pages | : 381 |
| Release | : 1983-11-02 |
| Genre | : Computers |
| ISBN | : 0080956718 |
Introduction to Sensitivity and Stability Analysis in Nonlinear Programming
| Author | : S. Zlobec |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 329 |
| Release | : 2013-11-21 |
| Genre | : Business & Economics |
| ISBN | : 1461500117 |
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.
| Author | : Brian Beavis |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 1990 |
| Genre | : Economics, Mathematical |
| ISBN | : 9780521336055 |
This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics central to economic analysis since the latter is so much concerned with the optimizing behaviour of economic agents and the stability of the interaction processes to which this gives rise. The topics covered include convexity, mathematical programming, fixed point theorems, comparative static analysis and duality, the stability of dynamic systems, the calculus of variations and optimal control theory. The authors present a more detailed and wide-ranging discussion of these topics than is to be found in the few books which attempt a similar coverage. Although the text deals with fairly advanced material, the mathematical prerequisites are minimised by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra. A novel feature of the book is that it provides the reader with an understanding and feel for the kinds of mathematical techniques most useful for dealing with particular economic problems. This is achieved through an extensive use of a broad range of economic examples (rather than the numerical/algebraic examples so often found). This is suitable for use in advanced undergraduate and postgraduate courses in economic analysis and should in addition prove a useful reference work for practising economists.
| Author | : Anthony V. Fiacco |
| Publisher | : CRC Press |
| Total Pages | : 460 |
| Release | : 2020-09-24 |
| Genre | : Mathematics |
| ISBN | : 1000153665 |
Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.
| Author | : Fiacco |
| Publisher | : CRC Press |
| Total Pages | : 174 |
| Release | : 2020-09-24 |
| Genre | : Mathematics |
| ISBN | : 1000153436 |
This book presents theoretical results, including an extension of constant rank and implicit function theorems, continuity and stability bounds results for infinite dimensional problems, and the interrelationship between optimal value conditions and shadow prices for stable and unstable programs.
| Author | : J.-B. Hiriart-Urruty |
| Publisher | : Elsevier |
| Total Pages | : 337 |
| Release | : 1986-01-01 |
| Genre | : Mathematics |
| ISBN | : 0080872409 |
Optimization, as examined here, ranges from differential equations to problems arising in Mechanics and Statistics. The main topics covered are: calculations of variations and nonlinear elasticity, optimal control, analysis and optimization in problems dealing with nondifferentiable data, duality techniques, algorithms in mathematical programming and optimal control.
| Author | : Miguel A. Goberna |
| Publisher | : |
| Total Pages | : 380 |
| Release | : 1998-03-11 |
| Genre | : Mathematics |
| ISBN | : |
A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover: * Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. * Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. * Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. * Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.
| Author | : E. de Klerk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 287 |
| Release | : 2006-04-18 |
| Genre | : Computers |
| ISBN | : 0306478196 |
Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming. In this monograph the basic theory of interior point algorithms is explained. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the Lovász theta function and the MAX-CUT approximation algorithm by Goemans and Williamson. Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.
