Introduction to Sensitivity and Stability Analysis in Nonlinear Programming PDF Download

Author: Fiacco
Publisher: Academic Press
ISBN: 0080956718
Category : Computers
Languages : en
Pages : 381

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Book Description
Introduction to Sensitivity and Stability Analysis in Nonlinear Programming

Author: Anthony V. Fiacco
Publisher:
ISBN:
Category : Nonlinear programming
Languages : en
Pages : 34

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Book Description
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:
ISBN:
Category : Nonlinear programming
Languages : en
Pages : 367

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Book Description

Author: Anthony V. Fiacco
Publisher: SIAM
ISBN: 9781611971316
Category : Mathematics
Languages : en
Pages : 226

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Book Description
Recent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the "central" or "dual" trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them.

Author: Alfred Auslender
Publisher: North Holland
ISBN:
Category : Computers
Languages : en
Pages : 196

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Book Description
This study collects the papers presented at the Nonlinear Analysis and Optimization conference held at the Center for Operations Research and Econometrics (CORE) in Louvain-la-Neuve, Belgium. It was the firm belief of the organizers of the meeting that there is a natural interaction between the methods used in nonlinear analysis and the problems encountered in optimization, and that gathering the papers into one book would be beneficial for both parties concerned. The papers are mainly concerned with the following themes: nonlinear analysis, sensitivity (stability) analysis and algorithms in nonlinear programming (for smooth, nonsmooth and global problems).

Author: Anthony V. Fiacco
Publisher:
ISBN:
Category : Mathematical optimization
Languages : en
Pages : 51

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Book Description
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: S. Zlobec
Publisher: Springer Science & Business Media
ISBN: 9780792371397
Category : Business & Economics
Languages : en
Pages : 378

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Book Description
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
ISBN: 9783728123947
Category : Computers
Languages : en
Pages : 274

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Book Description

Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
ISBN: 0387747583
Category : Mathematics
Languages : en
Pages : 4646

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Book Description
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
ISBN: 1489975942
Category : Business & Economics
Languages : en
Pages : 512

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Book Description
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.