Sensitivity analysis in convex programming
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TL;DR: The results in the paper prove that the sensitivity of the program depends on the solution of a dual program and its sensitivity.
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Abstract: The object of this paper is to perform an analysis of the sensitivity for convex vector programs with inequality constraints by examining the quantitative behavior of a certain set of optima according to changes of right-hand side parameters included in the program. The results in the paper prove that the sensitivity of the program depends on the solution of a dual program and its sensitivity.
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Citations
Sensitivity Analysis in Convex Optimization through the Circatangent Derivative
TL;DR: It is shown that the sensitivity of a vector convex optimization problem according to variations in the right-hand side is closely related to a Lagrange multiplier solution of a dual program.
On higher-order proto-differentiability and higher-order asymptotic proto-differentiability of weak perturbation maps in parametric vector optimization
TL;DR: In this article, the authors study higher-order sensitivity analysis in parametric vector optimization problems, and verify that the weak efficient solution map and the weak perturbation map of a parameterized vector optimization problem are higher order proto-differentiable/higher-order asymptotic protodifferentiable under some suitable qualification conditions.
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Sensitivity Analysis in Differential Programming through the Clarke Derivative
TL;DR: In this article, the sensitivity analysis in multiobjective differential programs with equality constraints was studied and the sensitivity of the program was measured by a Lagrange multiplier plus a projection of its derivative.
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Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization
TL;DR: In this paper, sensitivity analysis in terms of variational sets/asymptotic variational set for parametric vector optimization has been studied, and the relation between the above sets and the proper minima of a set-valued map and its profile map has been established.
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Variational Analysis, Optimization, and Fixed Point Theory
TL;DR: In the last two decades, the theory of variational analysis including variational inequalities (VI) emerged as a rapidly growing area of research because of its applications in nonlinear analysis, optimization, economics, game theory, and so forth; see, for example, as mentioned in this paper.
References
Lectu re Notes in Economics and Mathematical Systems
M. Beckmann,H. P. Kunzi +1 more
- 01 Jan 1975
Abstract: This series reports on new developments in mathematical economics, economic theory, econometrics, operations research and mathematical systems. The series welcomes proposals for: 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Seminars on topics of current research 4. Reports of meetings provided they are of exceptional interest and devoted to a single topic. In the case of a research monograph, or of seminar notes, the timeliness of a manuscript may be more important than its form, which may be preliminary or tentative. Manuscripts should be no less than 150 and preferably no more than 500 pages in length. The series and the volumes published in it are indexed by Scopus and ISI (selected volumes).
Contingent derivative of the perturbation map in multiobjective optimization
TL;DR: In this article, a weaker notion of set-valued derivative was introduced to improve Tanino's results by using weaker conditions, and it was shown that MinDG⊂DW under weaker conditions can be obtained under certain conditions.
102
Sensitivity analysis in multiple objective linear programming: the tolerance approach
TL;DR: In this article, the authors consider a multiple objective linear program solved by the weighted-sum approach and propose a method to determine the maximum percentage by which all weights can deviate simultaneously and independently from their estimated values while retaining the same optimal basis.
53
Nonscalarized multiobjective global optimization
TL;DR: In this article, a non-calarized vector cost function is used to solve vector optimization problems with non-conconcilable objectives, which is made possible due to the ability to obtain full global optimal solutions.
48
Sensitivity Analysis in MCDM
Tetsuzo Tanino
- 01 Jan 1999
TL;DR: This chapter will explain several approaches, though limited, to stability and sensitivity analysis in MCDM.
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