二阶锥互补问题的一类新的效益函数与全局误差界

A New Class of Merit Functions for SOCP and the Global Error Bound

基于广义Fischer-Burmeister函数对二阶锥互补问题(SOCCP)引入了一种新的效益函数:ψαp(x,y):=α2‖(xy)+‖2+12‖φp(x,y)‖2,其中α>1,p∈(1,∞)。在函数F是强单调的假设下,建立了二阶锥互补问题的一个全局误差界,并证明了此类效益函数的水平有界性。

In this paper,based on the generalized Fischer-Burmeister function,a new class of merit functions for second-order coneα1programming（SOCCP in short）is introduced which isψαp（x,y）：=‖（xy）＋ ‖2＋‖2φp（x,y）‖2,whereα1,p∈（1,∞）.2Under the assumption of Fis strong monotonous,it is verified that the proposed new kind of merit functions provide an error bound for the SOCCP and possess level boundedness.