## Smoothing functions for second-order-cone complementarity problems.(English)Zbl 0995.90094

The paper presents an alternative interior point approach for the nonlinear complementarity problem. The main interest of the results are in the area of optimization problems with Second Order Cone (SOC) constraints in $$\mathbb{R}^n$$, $$n\geq 1$$, the Lorentz cone. The usual problem is reformulated as a semidefinite cone constraints plus a constraint subspace. A smoothing function permits to model it by means of a non interior continuation method. The Jordan algebra and the functions associated with the SOC are characterized. Some smoothing functions are proposed and studied.

### MSC:

 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C30 Nonlinear programming 65K05 Numerical mathematical programming methods
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