A New Class Of Merit Functions For
The Nonlinear Complementarity Problem
Zhi-Quan Luo and Paul Tseng
The paper considers a new class of merit functions for the nonlinear
complementarity problem (NCP). A merit function from this class has
nice differentiability and convexity properties and, in the monotone
case, each of its stationary points is a solution of the NCP. In
general, a certain regularity condition is both necessary and
sufficient for a stationary point to be a solution of the NCP. In
addition, under suitable conditions, this merit function provides a
local/global error bound for the NCP and/or has bounded level sets.
In the monotone case, this merit function has a derivative-free
descent direction. Using this direction, we develop a practical
descent method for solving the NCP and we report our numerical
experience with this method.
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