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LFS functions in multi-objective programming

Luka Neralić, Sanjo Zlobec (1996)

Applications of Mathematics

We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where...

Linear combinations of partitions of unity with restricted supports

Christian Richter (2002)

Studia Mathematica

Given a locally finite open covering of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation f = C a C φ C with a C E and a partition of unity φ C : C subordinate to . As an application, we determine the class of all functions f ∈ C(||) on the underlying space || of a Euclidean complex such that, for each polytope P ∈ , the restriction f | P attains its extrema at vertices of P. Finally, a class of extremal functions on the metric space...

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