Abstract: The present paper presents a new problem, whose object is multiobjective and whose constraint is nonlinear inequality and variationa l inequality. This problem belongs to MPEC problem (mathematical programs with e quilibrium constraints), whose sufficient and necessary optimalit y conditons are given in this paper. By means of this su fficient condition the VPEC problem is transfered to a usual optimizational prob lem with constraints. An algorithm to solve this problem, i.e., the l¹ penalty function is given. In the end an example is given.

Key words: VPEC problem, variational inequality, l¹ penalty function, KKT conditions