Smoothing functions for second-order-cone complementarity problems (Q2784419)

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.