Research Of Smoothing Newton Methods For The Second Order Cone Programming Dual Problem

The second-order cone programming problem is to minimize or maximize a linear functionover the intersection of an affine space with the Cartesian product of a finite number ofsecond-order cones.Many cases is difficult to directly solve the problem of second-order cone,then to study its Dual problem, At this time by studying its dual problem to solving second-ordercone of the original problem is very meaningful.Based on the Fischer-Burmeister function and CHKS function proposed two newsmoothing functions.Then combined with two order cone programming and its dual problemoptimality conditions proposed a new Newton algorithm,transformed second-order coneprogrmming into a nonlinear equations and solve it. The advantage of this algorithm is that theinitial point selection requirements are relatively loose, meet the global convergence,with thesecond-order convergence rate. Numerical experiments demonstrate the fessibility and efficiencyof the functions.