二阶锥互补问题的一类效益函数与全局误差界

A class of merit functions for the second-order cone complementarity problems and a global error bound

二阶锥互补问题的一种常用解决方法是将它转化为某一效益函数的无约束极小化问题进行求解,效益函数的选取对这种方法的有效性起着很重要的作用.为此提出了二阶锥互补问题的一类效益函数,这类效益函数具有一些很好的性质.在某些条件下,基于这类效益函数建立了二阶锥互补问题解的一个全局误差界及这类函数的水平有界性.另外,还给出了这类效益函数的两个具体函数,并证明了这两个函数满足这些条件.

A popular approach to solving the second-order cone complementarity problem is to reformulate it as an unconstrained minimization problem of a certain merit function. The choice of merit function is important for the approach to be effective. A class of merit function is proposed for the second-order cone complementarity problem. These merit functions have some interesting properties. Under some suitable assumptions, a global error bound for the solution to the second-order cone complementarity problem is established and the level of every merit function is bounded based on these merit functions. Moreover, two specific functions of the class are presented and demonstrated to satisfy these assumptions.