A General Scalar-Valued Gap Function for Nonsmooth Multiobjective Semi-Infinite Programming

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints, we define a new gap function that generalizes the definitions of this concept in other articles. Then, we characterize the efficient, weakly efficient, and properly efficient solutions of the problem utilizing this new gap function. Our results are based on $(Phi,rho)-$invexity, defined by Clarke subdifferential.