Two New Smoothing Algorithms For Linear Second-Order Cone Programming

In this thesis,linear second-order cone programming problems are studied.These problems are widely used,such as in signal processing,investment portfolio,image processing,acoustics,neural network and so on.Thus,it is of great significance for the research on the algorithm of linear second-order cone programming both in theory and in practical applications.In this thesis,two new smoothing Newton algorithms for linear secondorder cone programming are proposed.One is the monotone smoothing Newton algorithm.Firstly,a new smoothing complementary function with parameter is proposed based on the Fischer-Burmeister(FB)complementary function.When parameter selection value is different,the complementary function has the characteristic of degenerating into different smoothing FB complementary functions.Secondly,it is transformed into a nonlinear system of equations by using the algebraic theory related to the second-order cone.At the same time,a new algorithm for the linear second-order cone programming is given by combining line search technique and the fitness of the algorithm is analyzed.Finally,under the appropriate conditions,the convergence of the algorithm is analyzed.Numerical experiments show that the algorithm is feasible and effective.Another is the non-monotone smoothing Newton algorithm.Non-monotone smoothing Newton method has the advantage of bypassing some minimal points to improve the overall efficiency of the algorithm and obtain better numerical results.At first,a new smoothing complementary function with parameter is proposed based on the FB and Natural-Residual(NR)complementary functions.When parameter selection value is different,the complementary function has the characteristic of degenerating into smoothing FB and Chen-Harker-Kanzow-Smale(CHKS)complementary functions.Then,a non-monotonous smoothing Newton algorithm that combined with line search technique is presented.And the fitness of the algorithm is analyzed.At last,under the appropriate conditions,the convergence of the algorithm is analyzed.Numerical experiments show that the algorithm is feasible and effective.