Well-posedness for multi-time variational inequality problems via generalized monotonicity and for variational problems with multi-time variational inequality constraints

The present paper investigates the well-posedness associated with multi-time variational inequality problems and the corresponding variational problems involving aforesaid inequality as a constraint. Firstly, we introduce the multi-time variational inequality problems determined by curvilinear integral functionals. Thereafter, we present the metric characterization of well-posedness in terms of approximate solution by defining the generalized monotonicity for the considered multi-time functional. Also, we establish that the well-posedness is equivalent to the existence and uniqueness of solution for the problems under consideration. Moreover, the mathematical development is accompanied by various illustrative examples. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the well-posedness of multi-time variational inequality problems and the corresponding variational problems. By introducing the multi-time variational inequality problems determined by curvilinear integral functionals and defining generalized monotonicity to measure the well-posedness, it is proven that the well-posedness is equivalent to the existence and uniqueness of solution. The mathematical development is accompanied by various illustrative examples.