  A merit (gap) function is a map that returns zero at the solutions of
problems and strictly positive values otherwise. Its minimization is equivalent
to the original problem by definition, and it can estimate the distance between
a given point and the solution set. Ideally, this function should have some
properties, including the ease of computation, continuity, differentiability,
boundedness of the level set, and error boundedness. In this work, we propose
new merit functions for multiobjective optimization with lower semicontinuous
objectives, convex objectives, and composite objectives, and we show that they
have such desirable properties under reasonable assumptions.
