In Andreani et al. (Numer. Algorithms 57:457–485, 2011), an interior point method for the horizontal nonlinear complementarity problem was introduced. This method was based on inexact Newton directions and safeguarding projected gradient iterations. Global convergence, in the sense that every cluster point is stationary, was proved in Andreani et al. (Numer. Algorithms 57:457–485, 2011). In Andreani et al. (Eur. J. Oper. Res. 249:41–54, 2016), local fast convergence was proved for the underdetermined problem in the case that the Newtonian directions are computed exactly. In the present paper, it will be proved that the method introduced in Andreani et al. (Numer. Algorithms 57:457–485, 2011) enjoys fast (linear, superlinear, or quadratic) convergence in the case of truly inexact Newton computations. Some numerical experiments will illustrate the accuracy of the convergence theory.
Horizontal complementarity problems Interior point methods Global convergence Inexact Newton method Projected gradients Local convergence
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Fernandes, L., Friedlander, A., Guedes, M.C., Júdice, J.: Solution of a general linear complementarity problem using smooth optimization and its applications to bilinear programming and LCP. Appl. Math. Optim 43, 1–19 (2001)MathSciNetCrossRefMATHGoogle Scholar