Growth behavior of two classes of merit functions for symmetric cone complementarity problems (Q1029282)

The authors consider properties of the merit functions suggested in the works by \textit{Y. G.~Evtushenko} and \textit{V. A.~Purtov} [Sov. Math. Dokl. 30, 313--316 (1984; Zbl 0621.90062)] and by \textit{O. L.~Mangasarian} and \textit{M. V.~Solodov} [Math. Program. 62, No. 2 (B), 277--297 (1993; Zbl 0813.90117)], which are applied to symmetric cone complementarity problems. They show that all the merit functions are coercive in the linear case if the underlying linear transformation has the P-property. In the nonlinear case the coercivity requires the uniform Jordan P-property and some additional continuity properties for the second kind of the merit functions. These results extend the previous ones obtained by \textit{P.~Tseng} [J. Optimization Theory Appl. 89, No.1, 17--37 (1996; Zbl 0866.90127)] and by \textit{C.~Kanzow} and \textit{M.~Fukushima} [Math. Program. 83, No.1 (A), 55--87 (1998; Zbl 0920.90134)] from the case of the usual complementarity problem.