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39 reviewsVariational inequalities proved to be a very useful tool for investigation and solution of various equilibrium type problems arising in Economics, Operations Research, Mathematical Physics, and Transportation. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relaxation approach. This approach is rather flexible and allows one to construct various methods both for single-valued and for multi-valued variational inequalities, including nonlinear constrained problems. The other essential feature of the combined relaxation methods is that they are convergent under very mild assumptions. The book can be viewed as an attempt to discribe the existing combined relaxation methods as a whole.
In this chapter, we consider basic schemes of combined relaxation (CR) methods and implementable algorithms for solving variational inequality problems with continuous single-valued mappings under a finite-dimensional space setting. Variational inequalities proved to be a very useful and powerful tool for in vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics. Variational inequalities proved to be a very useful and powerful tool for in vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics.