Abstract
In this paper, we show that the parametric general nonconvex variational inequalities are equivalent to the parametric Wiener-Hopf equations. We use this alternative equivalent formulation to study the sensitivity analysis for the nonconvex variational inequalities without assuming the differentiability of the given data. Our results can be considered as a significant extension of previously known results for the variational inequalities.
Highlights
1 Introduction Variational inequalities theory, which was introduced by Stampacchia [ ], provides us with a simple, natural, general and unified framework to study a wide class of problems arising in pure and applied sciences; see [ – ]
This technique has been modified and extended by many authors for studying the sensitivity analysis of other classes of variational inequalities and variational inclusions. It is known [ ] that the variational inequalities are equivalent to the Wiener-Hopf equations. This alternative equivalent formulation has been used by Noor [ ] and Noor et al [, ] to develop the sensitivity analysis framework for various classes of variational inequalities
We develop the general framework of sensitivity analysis for the general nonconvex variational inequalities
Summary
Variational inequalities theory, which was introduced by Stampacchia [ ], provides us with a simple, natural, general and unified framework to study a wide class of problems arising in pure and applied sciences; see [ – ]. It is known [ ] that the variational inequalities are equivalent to the Wiener-Hopf equations. We first establish the equivalence between parametric general nonconvex variational inequalities and the parametric Wiener-Hopf equations by using the projection technique.
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