New merit functions for multiobjective optimization and their properties

AbstractA 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.Keywords: Multiobjective optimizationmerit functionsPareto stationarityerror boundscomposite optimizationAMS Classifications: 90C2990C30 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by the Grant-in-Aid for Scientific Research (C)(21K11769 and 19K11840) and Grant-in-Aid for JSPS Fellows (20J21961) from Japan Society for the Promotion of Science.