We study mathematical programs with complementarity constraints. Several stationarity concepts, based on a piecewise smooth formulation, are presented and compared. The concepts are related to stationarity conditions for certain smooth programs as well as to stationarity concepts for a nonsmooth exact penalty function. Further, we present Fiacco-McCormick type second order optimality conditions and an extension of the stability results of Robinson and Kojima to mathematical programs with complementarity constraints.

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Data envelopment analysis (DEA) is a methodology that allows, in one way or other, the assignment of efficiency scores to members of a group of decision-making units. We call an efficiency measure “continuous” if small perturbations of the input-output data cause only small changes in the score. Continuity is a desirable property of an efficiency measure, in particular in the presence of measurement tolerances. Continuity is also desirable from a numerical point of view because the scores are computed by linear programming software. Focusing on convex production possibility sets, we give examples where radial DEA measures fail to be continuous, i.e., they “jump” under small data perturbations. We present necessary and sufficient conditions for continuity in terms of the data and show that these conditions are satisfied for “almost all” data. We also discuss continuity of nonradial measures and identify possible problems of “multistage approaches” to compute mix efficiencies.

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Dicopper(i) complexes with the chelating dmapm ligand [dmapm = 1,1-bis{di(o-N,N-dimetylanilinyl)phosphino}methane] have been synthesized and characterized structurally. Synthesis of the acetonitrile adduct [Cu2(μ-dmapm)(CH3CN)2][BF4]2 () has been presented and the dicopper electrophile has been used as the starting material in reaction with Group 14 heteroborates. Coordination of the closo-borates at the dicopper moiety resulted in different molecular structures with varying CuCu distances. In the case of the side on coordinated stanna-closo-dodecaborate the tin vertex has been characterized by (119)Sn Mössbauer spectroscopy and the nucleophilicity at the tin was established in reaction with a molybdenum carbonyl complex.