A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem. (27th March 2013) - Gui, Zhuqing; Hu, Chunyan; Zhu, Zhibin
Abstract : Firstly, we give the Karush-Kuhn-Tucker (KKT) optimality condition of primal problem and introduce Jordan algebra simply. On the basis of Jordan algebra, we extend smoothing Fischer-Burmeister (F-B) function to Jordan algebra and make the complementarity condition smoothing. So the first-order optimization condition can be reformed to a nonlinear system. Secondly, we use the mixed line search quasi-Newton method to solve this nonlinear system. Finally, we prove the globally and locally superlinear convergence of the algorithm.