Nonsymmetric cone program and its corresponding complementarity problem have long been mysterious to optimization researchers because of no unified analysis technique to handle these cones. Nonetheless, merit function approach is a popular method to deal with general conic complementarity problem, for which the key lies on constructing appropriate merit functions. In this paper, we focus on a special class of nonsymmetric cone complementarity problem, that is, the ellipsoidal cone complementarity problem (ECCP). We not only show the readers how to construct merit functions for solving the ellipsoidal cone complementarity problem, but also we study the conditions under which the level sets of the corresponding merit functions are bounded. In addition, we assert that these merit functions provide an error bound for the ellipsoidal cone complementarity problem. All these results build up a theoretical basis for the merit function method for solving ellipsoidal cone complementarity problem.
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