A REGULATED NEWTON METHOD FOR THE COMPLEMENTARITY PROBLEM OVER EUCLIDEAN JORDAN ALGEBRA WITH SECOND-ORDER CONES

In this paper, the second-order cone complementarity problem is transformed into a system of algebraic equations by applying the Fischer-Burmeister function. A regulated Newton method is presented to obtain numerical solutions of the problem. By this method, we only need to solve a system of equations at each iteration, without performing any line search. The condition P-0-property is weaker than monotonicity or Cartesian P-0-property which was usually used in existing methods. The validity of the modified technique is shown by illustrative examples and numerical solutions of the problem are calculated with readily computable components. The approximate solutions converge to the exact solution more rapidly than the existing smoothing Newton method.