On gap functions for nonsmooth multiobjective optimization problems

A set-valued gap function, g, existing in the literature for smooth and nonsmooth multiobjective optimization problems is dealt with. It is known that 0 € d(1*)is a sufficient condition forefficiency of a feasible solution r*, while the converse does not hold. In the current work, the converse of this assertion is proved for properly efficient solutions. Afterwards, to avoid the complexities of set-valued maps some new single-valued gap functions, for nonsmooth multiobjective optimization problems with locally Lipschitz data are introduced. Important properties of the new gap functions are established.