  A multiobjective optimization problem is simplicial if the Pareto set and
front are homeomorphic to a simplex and, under the homeomorphisms, each face of
the simplex corresponds to the Pareto set and front of a subproblem. In this
paper, we show that strongly convex problems are simplicial under a mild
assumption on the ranks of the differentials of the objective mappings. We
further prove that one can make any strongly convex problem satisfy the
assumption by a generic linear perturbation, provided that the dimension of the
source is sufficiently larger than that of the target. We demonstrate that the
location problems, a biological modeling, and the ridge regression can be
reduced to multiobjective strongly convex problems via appropriate
transformations preserving the Pareto ordering and the topology.
