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Author: Robert L. Armacost
Publisher:
ISBN:
Category : Inventory control
Languages : en
Pages : 44
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Book Description
Recently, it has been shown that a class of penalty function algorithms can readily be adapted to generate sensitivity analysis information for a large class of parametric nonlinear programming problems. In particular, estimates of the partial derivatives (with respect to the problem parameters) of the components of a solution vector and the optimal value function have been successfully calculated for a number of nontrivial examples. The approach has been implemented using the well known Sequential Unconstrained Minimization Technique (SUMT) computer program. This paper, a continuation and amplification of a recent paper by Armacost, gives a detailed summary of the significant underlying theoretical results, reviews recent additions to the computer program that include Lagrange multiplier sensitivity calculations, and elaborates on the kind of information that can be generated by further analyzing and interpreting results obtained in applying the techique to a well known inventory model. (Author).
Author: Robert L. Armacost
Publisher:
ISBN:
Category : Inventory control
Languages : en
Pages : 44
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Book Description
Recently, it has been shown that a class of penalty function algorithms can readily be adapted to generate sensitivity analysis information for a large class of parametric nonlinear programming problems. In particular, estimates of the partial derivatives (with respect to the problem parameters) of the components of a solution vector and the optimal value function have been successfully calculated for a number of nontrivial examples. The approach has been implemented using the well known Sequential Unconstrained Minimization Technique (SUMT) computer program. This paper, a continuation and amplification of a recent paper by Armacost, gives a detailed summary of the significant underlying theoretical results, reviews recent additions to the computer program that include Lagrange multiplier sensitivity calculations, and elaborates on the kind of information that can be generated by further analyzing and interpreting results obtained in applying the techique to a well known inventory model. (Author).
Author: Anthony V. Fiacco
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 64
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Book Description
In the paper the author establishes a theoretical basis for using a penalty-function method to estimate sensitivity information (i.e., the partial derivatives) of a local solution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions. The local solution is assumed to satisfy the second order sufficient conditions for a strict minimum. Although theoretically valid for higher order derivatives, tha analysis concentrates on the estimation of the first order (first partial derivative) sensitivity information, which can be explicitly expressed in terms of the problem functions. For greater clarity, the results are given in terms of the mixed logarithmic-barrier quadratic-loss function. However, the approach is clearly applicable to any twice-differentiable penalty-function algorithm. (Author).
Author: Robert L. Armacost
Publisher:
ISBN:
Category : Mathematical optimization
Languages : en
Pages : 59
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Book Description
Pursuing a number of theoretical results recently obtained by Fiacco, this paper continues the development of a basis for calculating first-order changes in a Kuhn-Tucker triple and second-order changes in the optimal value function of a class of general parametric nonlinear programming problems, with respect to a perturbation of the problem parameters. Exploiting problem structure, specific formulas are derived for calculating the first partial derivatives of a Kuhn-Tucker triple. Approximations to these quantities are obtained in parallel throughout, by way of an associated logarithmic-quadratic penalty function. Applications are indicated.
Author: Tomas Gal
Publisher: Springer Science & Business Media
ISBN: 1461561035
Category : Business & Economics
Languages : en
Pages : 595
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Book Description
The standard view of Operations Research/Management Science (OR/MS) dichotomizes the field into deterministic and probabilistic (nondeterministic, stochastic) subfields. This division can be seen by reading the contents page of just about any OR/MS textbook. The mathematical models that help to define OR/MS are usually presented in terms of one subfield or the other. This separation comes about somewhat artificially: academic courses are conveniently subdivided with respect to prerequisites; an initial overview of OR/MS can be presented without requiring knowledge of probability and statistics; text books are conveniently divided into two related semester courses, with deterministic models coming first; academics tend to specialize in one subfield or the other; and practitioners also tend to be expert in a single subfield. But, no matter who is involved in an OR/MS modeling situation (deterministic or probabilistic - academic or practitioner), it is clear that a proper and correct treatment of any problem situation is accomplished only when the analysis cuts across this dichotomy.
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: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 252
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Book Description
Author: Robert Leo Armacost
Publisher:
ISBN:
Category : Nonlinear programming
Languages : en
Pages : 508
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Book Description
Author: Fiacco
Publisher: CRC Press
ISBN: 1000153436
Category : Mathematics
Languages : en
Pages : 174
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Book Description
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: BANK
Publisher: Birkhäuser
ISBN: 3034863284
Category : Science
Languages : en
Pages : 227
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Book Description
Author: Malamas Caracotsios
Publisher:
ISBN:
Category :
Languages : en
Pages : 424
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Book Description
