Simpliciality of strongly convex problems

A multiobjective optimization problem is $C^r$ simplicial if the Pareto set and front are diffeomorphic to a simplex and, under diffeomorphisms, each face of corresponds subproblem, where $0 \leq r \infty$. In paper titled “Topology sets strongly convex problems”, it has been shown that $C^{r-1}$ mild assumption on ranks differentials mapping for $2 On other hand, in this paper, we show $C^1$ $C^0$ same assumption. Moreover, establish specialized transversality theorem generic linear perturbations $(r \geq 2)$. By theorem, also give an application singularity theory