Image Space Analysis for Vector Optimization and Variational Inequalities: Scalarization

Vector constrained extremum problems and Vector Variational Inequalities are considered, and a separation scheme is introduced. Starting from such a scheme, several theoretical aspects can be developed as well as methods of solution; for instance, scalarization of Vector Optimization is analysed and a method is described which does not require any assumption on the problem. The analysis is extended to a Vector Variational Inequality; this turns out to be equivalent to a scalar Quasi–Variational Inequality.