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**Properties of restricted NCP functions for nonlinear complementarity problems.**
*(English)*
Zbl 0913.90253

Summary: We study restricted NCP functions which may be used to reformulate the nonlinear complementarity problem as a constrained minimization problem. In particular, we consider three classes of restricted NCP functions, two of them introduced by Solodov and the other proposed in this paper. We give conditions under which a minimization problem based on a restricted NCP function enjoys favorable properties, such as equivalence between a stationary point of the minimization problem and the nonlinear complementarity problem, strict complementarity at a solution of the minimization problem, and boundedness of the level sets of the objective function. We examine these properties for three restricted NCP functions and show that the merit function based on the restricted NCP function proposed in this paper enjoys favorable properties compared with those based on the other restricted NCP functions.

### MSC:

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

### Keywords:

bounded level sets; nonlinear complementarity; constrained minimization; restricted NCP functions; stationary point; merit function
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\textit{N. Yamashita}, J. Optim. Theory Appl. 98, No. 3, 701--717 (1998; Zbl 0913.90253)

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### References:

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