In the last fifteen years the so-called equilibrium problem has been extensively studied within nonlinear analysis especially due to its important particular cases such as optimization problems, saddle point/minimax problems, variational and hemivariational inequalities, these problems are useful models of many practical situations arising in economics, engineering, physics, chemistry, etc. In the last decade one could observe a growing interest upon the vector equilibrium problems, which provide a unifying framework for investigating a large variety of problems like vector optimization (useful in economics) and vector variational inequalities

The aim of this project is to make a comprehensive study on the equilibrium problems and their particular cases, both the scalar and vector versions. The purposes have been formulated within ten different, but not independent problems. The most of them are originated from the results published by the research team of the project and concern investigations (among others) upon the stability of solutions of the equilibrium problems, the algorithms for solving variational inequalities, duality of the equilibrium problems, the homogenization problems and the monotonicity in connection with variational inequalities. Our research is based both on own and other's results known in the literature. During the whole period we intend to keep our strong connections with mathematicians from abroad, those who already contributed in developing these subject.