Aubin property and uniqueness of solutions in cone constrained optimization

We discuss conditions for the Aubin property of solutions to perturbed cone constrained programs, by using and refining results given in Klatte and Kummer (Nonsmooth equations in optimization. Kluwer, Dordrecht, 2002). In particular, we show that constraint nondegeneracy and hence uniqueness of the multiplier is necessary for the Aubin property of the critical point map. Moreover, we give conditions under which the critical point map has the Aubin property if and only if it is locally single-valued and Lipschitz.     

On a Frank-Wolfe type theorem in cubic optimization

ABSTRACT

A classical result due to Frank and Wolfe [An algorithm for quadratic programming. Naval Res Log Quart. 1956;3:95–110] says that a quadratic function f attains its supremum on a nonempty polyhedron M if f is bounded from above on M. In this note, we present a stringent proof of the extension of this result to cubic optimization (known from Andronov, Belousov and Shironin [On solvability of the problem of polynomial programming (In Russian). Izvestija Akadem. Nauk SSSR, Tekhnicheskaja Kibernetika. 1982;4:194–197. Translation appeared in News of the Academy of Science of USSR, Dept. of Technical Sciences, Technical Cybernetics.]). Further, we discuss related results. In particular, we bring back to attention Kummer's [Globale Stabilität quadratischer Optimierungsprobleme. Wissenschaftliche Zeitschrift der Humboldt- Universität zu Berlin, Math-Nat R. 1977;XXVI(5):565–569] generalization of the Frank-Wolfe theorem to the case that f is quadratic, but M is the Minkowski sum of a compact set and a polyhedral cone.     

Die Universalität der Kuspoiden

Ohne Zusammenfassung     

Numerische Lösung eines ebenen Anfangswertproblems aus dem Gebiet der Wasserwellen

Zusammenfassung Ein spezielles Wasserwellenproblem wird mit einem mathematischen Verfahren gelöst, das alle auf dem freien Rand vorgegebenen Bedingungen exakt erfüllt. Die Methode kann auch auf andere Probleme angewandt werden, wie eine Nachfolgearbeit über ein Kavitationsproblem zeigt.

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Summary A special water-wave problem is solved by a mathematical method which satisfies all free surface conditions exactly. The method can be applied to other problems as a following paper about a cavity problem shows.

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Diese Arbeit entstand in der Gesellschaft für wissenschaftliche Datenverarbeitung m.b.H. Göttingen.     

Synthesis and Reactivity of 2‐Pyrrolidino‐, 2‐N‐Methylpiperazino‐, 2‐Piperidino‐, and 2‐Morpholino‐1,3,4‐thiadiazines

A variety of 2‐pyrrolidino‐, 2‐N‐methylpiperazino‐, 2‐piperidino‐, and 2‐morpholino‐1,3,4‐thiadiazines were prepared by cyclocondensation of phenacyl halides with thiosemicarbazides. Heating of the products resulted in desulfurization and formation of pyrazoles. The rate of this process strongly depends on the substitution pattern of the 1,3,4‐thiadiazines.     

Periodicity in collision-induced and remote-bond activation of alkali metal ions attached to polyether ionophores

The collision-induced dissociation of lasalocid and monensin A bound to alkali metal cations has been investigated using electrospray MS/MS. The binding affinity for the metal cations, as measured with collision-induced dissociation, was found to depend on their ionic radius, decreasing with increasing radius. Monensin A was observed to have a greater binding affinity for alkali metal cations than lasalocid acid.