Author : Fiacco
Publisher : Academic Press
Page : 381 pages
File Size : 23,17 MB
Release : 1983-11-02
Category : Computers
ISBN : 0080956718
Introduction to Sensitivity and Stability Analysis in Nonlinear Programming
Author : Anthony V. Fiacco
Publisher :
Page : 34 pages
File Size : 22,63 MB
Release : 1990
Category : Nonlinear programming
ISBN :
We suggest several important research topics for semi-infinite programs whose problem functions and index sets contain parameters that are subject to perturbation. These include optimal value and optimal solution sensitivity and stability properties and penalty function approximation techniques. The approaches proposed are a natural carryover from parametric nonlinear programming, with emphasis on practical applicability and computability. Keywords: Semi-infinite programming, Perturbation analysis, Sensitivity analysis, Stability, Parametric non-linear programming, Penalty functions, Mathematical equations. (cp).
Author : Anthony V. Fiacco
Publisher :
Page : 367 pages
File Size : 11,62 MB
Release : 1983
Category : Nonlinear programming
ISBN :
Author : Anthony V. Fiacco
Publisher :
Page : 51 pages
File Size : 29,33 MB
Release : 1979
Category : Mathematical optimization
ISBN :
For large classes of mathematical programming problems, a detailed technical survey is given of key developments in sensitivity and stability analysis results, i.e., results characterizing the relationship between the optimal value function or a solution set and problem perturbations. The emphasis is on finite dimensional nonlinear problems with deterministic parametric perturbations. Precise assumptions and conclusions of key results are given in the more than 30 theorems that are stated. Some effort has been made to unify the notation and terminology and to place the results in perspective. Directions of future research and applications are indicated. Finally, an extensive bibliography is included. The paper is motivated by a desire to unify into one body of theory the many penetrating results that are now known in this crucially important area. (Author).
Author : M. Asghar Bhatti
Publisher : Springer Science & Business Media
Page : 711 pages
File Size : 12,67 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 1461205018
This introductory textbook adopts a practical and intuitive approach, rather than emphasizing mathematical rigor. Computationally oriented books in this area generally present algorithms alone, and expect readers to perform computations by hand, and are often written in traditional computer languages, such as Basic, Fortran or Pascal. This book, on the other hand, is the first text to use Mathematica to develop a thorough understanding of optimization algorithms, fully exploiting Mathematica's symbolic, numerical and graphic capabilities.
Author : S. Zlobec
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 35,8 MB
Release : 2001-08-31
Category : Business & Economics
ISBN : 9780792371397
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 : Simone Loureiro de Oliveira
Publisher : vdf Hochschulverlag AG
Page : 274 pages
File Size : 48,52 MB
Release : 1996
Category : Computers
ISBN : 9783728123947
Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 24,79 MB
Release : 2008-09-04
Category : Mathematics
ISBN : 0387747583
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Author : Terry L. Friesz
Publisher : Springer
Page : 512 pages
File Size : 22,76 MB
Release : 2015-09-30
Category : Business & Economics
ISBN : 1489975942
This is a book about infrastructure networks that are intrinsically nonlinear. The networks considered range from vehicular networks to electric power networks to data networks. The main point of view taken is that of mathematical programming in concert with finite-dimensional variational inequality theory. The principle modeling perspectives are network optimization, the theory of Nash games, and mathematical programming with equilibrium constraints. Computational methods and novel mathematical formulations are emphasized. Among the numerical methods explored are network simplex, gradient projection, fixed-point, gap function, Lagrangian relaxation, Dantzig-Wolfe decomposition, simplicial decomposition, and computational intelligence algorithms. Many solved example problems are included that range from simple to quite challenging. Theoretical analyses of several models and algorithms, to uncover existence, uniqueness and convergence properties, are undertaken. The book is meant for use in advanced undergraduate as well as doctoral courses taught in civil engineering, industrial engineering, systems engineering, and operations research degree programs. At the same time, the book should be a useful resource for industrial and university researchers engaged in the mathematical modeling and numerical analyses of infrastructure networks.
Author : Thomas Frederick Coleman
Publisher : American Mathematical Soc.
Page : 257 pages
File Size : 42,76 MB
Release : 2009
Category : Mathematics
ISBN : 0821844857
A large number of mathematical models in many diverse areas of science and engineering have lead to the formulation of optimization problems where the best solution (globally optimal) is needed. This book covers a small subset of important topics in global optimization with emphasis on theoretical developments and scientific applications.
