Growth Behavior of Two Classes of Merit Functions for Symmetric Cone Complementarity Problems

S. H. Pan () and J.-S. Chen ()
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S. H. Pan: South China University of Technology
J.-S. Chen: National Taiwan Normal University

Journal of Optimization Theory and Applications, 2009, vol. 141, issue 1, No 10, 167-191

Abstract: Abstract In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth implicit Lagrangian complementarity function, respectively. We show that, for the linear symmetric cone complementarity problem (SCLCP), both the EP merit functions and the implicit Lagrangian merit function are coercive if the underlying linear transformation has the P-property; for the general SCCP, the EP merit functions are coercive only if the underlying mapping has the uniform Jordan P-property, whereas the coerciveness of the implicit Lagrangian merit function requires an additional condition for the mapping, for example, the Lipschitz continuity or the assumption as in (45).

Keywords: Symmetric cone complementarity problem; Jordan algebra; EP merit functions; Implicit Lagrangian function; Coerciveness (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10957-008-9495-y

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