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We study here the crepant resolution correspondence for the torus equivariant descendent Gromov-Witten theories of Hilb(C2) and Sym(C2).The descendent correspondence is obtained from our previous matching of the associated CohFTs by applying Givental's quantization formula to a specific symplectic transformation K. The first result of the paper is an explicit computation of K. Our main result then establishes a fundamental relationship between the Fourier-Mukai equivalence of the associated derived categories (by Bridgeland, King, and Reid) and the symplectic transformation K via Iritani's integral structure. The results use Haiman's Fourier-Mukai calculations and are exactly aligned with Iritani's point of view on crepant resolution.

In this paper, we extend the one-parametric class of merit functions proposed by Kanzow and Kleinmichel [C. Kanzow, H. Kleinmichel, A new class of semismooth Newton-type methods for nonlinear complementarity problems, Comput. Optim. Appl. 11 (1998) 227251] for the nonnegative orthant complementarity problem to the general symmetric cone complementarity problem (SCCP). We show that the class of merit functions is continuously differentiable everywhere and has a globally Lipschitz continuous gradient mapping. From this, we particularly obtain the smoothness of the FischerBurmeister merit function associated with symmetric cones and the Lipschitz continuity of its gradient. In addition, we also consider a regularized formulation for the class of merit functions which is actually an extension of one of the NCP function classes studied by [C. Kanzow, Y. Yamashita, M. Fukushima, New NCP functions and