Journal Article10.1007/S00009-011-0143-7
Sensitivity Analysis in Differential Programming through the Clarke Derivative
8
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.
read more
Abstract: In this paper we deal with the sensitivity analysis in multiobjective differential programs with equality constraints. More specifically, we focused on analyzing the quantitative behavior of a certain set (non necessarily singleton) of optima according to changes of the right-hand side parameters. We prove that the sensitivity of the program is measured by a Lagrange multiplier plus a projection of its derivative. The sensitivity analysis is accomplished by utilizing the Clarke derivative, which transmits its characteristic stability to the obtained result.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Sensitivity analysis in parametric vector optimization in Banach spaces via τw-contingent derivatives
Thanh Tung Le,Thanh Hung Pham +1 more
TL;DR: In this article, the relationship between the τw-contingent derivative of the Borwein proper perturbation map and the γw-constraint derivative of feasible map in objective space is considered.
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.
7
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.
A natural extension of the classical envelope theorem in vector differential programming
TL;DR: The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming and shows that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.
Paratingent Derivative Applied to the Measure of the Sensitivity in Multiobjective Differential Programming
TL;DR: In this article, the sensitivity of differential programs of the form subject to where and are maps whose respective images lie in ordered Banach spaces is analyzed and the behavior of some nonsingleton sets of -optimal solutions according to changes of the parameter in the problem is analyzed.
References
•Book
Convex analysis and nonlinear optimization : theory and examples
Jonathan M. Borwein,Adrian S. Lewis +1 more
- 01 Jan 2000
TL;DR: In this paper, the Karush-Kuhn-Tucker Theorem and Fenchel duality were used for infinite versus finite dimensions, with a list of results and notation.
1.5K
•Book
Convex analysis and nonlinear optimization
Jonathan M. Borwein,Adrian S. Lewis +1 more
- 01 Jan 2006
940
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
Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems
Thai Doan Chuong,Jen-Chih Yao +1 more
TL;DR: In this article, the generalized Clarke epiderivative of the extremum point multifunction in parametric vector optimization problems is studied and an application to semi-infinite programming is given.
50
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.
30