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On the natural merit function for solving complementarity problems. (English) Zbl 1236.90127
The authors consider a general class of complementarity problems (CP’s) of the form $H(x,y,w)=0, x^{T}w=0, x,w \geq 0,$ containing the usual CP’s and investigate the problem of minimization of the natural merit function, which is the sum of squares of the gap components. They give conditions which provide for the stationary points of this problem to be solutions of the initial one. These conditions utilize non-singularity of the Jacobian or monotonicity type properties.

##### MSC:
 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C46 Optimality conditions and duality in mathematical programming 90C30 Nonlinear programming
SPG
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