Sensitivity analysis in multiobjective differential programming
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TL;DR: The aim of the paper is to investigate the derivative of certain set-valued maps of efficient points and show that the sensitivity depends on a set- valued map associated to the T-Lagrange multipliers and a projection of its sensitivity.
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Abstract: In this paper we deal with sensitivity analysis in multiobjective differential programs with equality constraints. We analyze the quantitative behavior of the optimal solutions according to changes of right-hand side values included in the original optimization problem. One of the difficulties lies in the fact that the efficient solution in multiobjective optimization in general becomes a set. If the preference of the decision maker is represented by a scalar utility which transforms optimal solutions in optima, we may apply existing methods of sensitivity analysis. However, when dealing with a subset of optimal points, the existence of a Frechet differentiable selection of such a set-valued map is usually assumed. The aim of the paper is to investigate the derivative of certain set-valued maps of efficient points. We show that the sensitivity depends on a set-valued map associated to the T-Lagrange multipliers and a projection of its sensitivity.
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Citations
Sensitivity analysis in convex programming
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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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.
Nonlinear Multiobjective Programming
Alexander Engau
- 15 Feb 2011
TL;DR: This introductory treatment of the theory and methodology of nonlinear multiobjective programming offers an annotated bibliographic overview of various concepts and approaches to solve continuous deterministic multicriteria optimization problems.
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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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The envelope theorem for multiobjective convex programming via contingent derivatives
TL;DR: In this article, the envelope theorem for vector convex programs is formulated and the sensitivity of a set of associated Lagrange multipliers and its sensitivity depends on a subset of associated parameters.
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References
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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.
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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.
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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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Sensitivity Analysis for Convex Multiobjective Programming in Abstract Spaces
TL;DR: In this article, it was shown that for a linear or convex multiobjective program, a dual program can be obtained which gives the primal sensitivity without any special hypothesis about the way of choosing the optimal solution in the efficient set.
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