对称锥互补问题的一类惩罚FB函数

A penalized FB function for symmetric cone complementarity problems

利用欧几里德若当代数技术,在单调的条件下,用内积的方法证明了对称锥互补问题的一类FB互补函数相应的势函数的水平集有界性.该方法在理论和应用上相较于以往用迹不等式证明势函数水平集有界性更具普适性和推广价值.在设计算法求解势函数的无约束极小化问题时,水平集有界性是保证下降算法收敛的重要条件,因此,对算法的设计具有理论意义.

With Euclidean Jordan algebras,we proved the level-boundedness of the merit function related to a penalized Fischer-Burmeister function for symmetric cone complementarity problems with monotonicity in a method of inner product.The method has more universality and promotion value both on theories and applications compared with previous trace inequality method to prove level-boundedness of the merit function.Level-boundedness plays an important part on a guarantee of decline algorithm convergence when we design algorithm to solve unconstrained minimization problem.Therefore,it has theoretical significance on the design of algorithm.