基于尺度中心路径的求解SCLP的非单调光滑牛顿算法

Non-Monotone Smoothing Newton Algorithm for SCLP Based on a Scaled Central Path

基于CHKS光滑函数的修改性版本,该文提出了一个带有尺度中心路径的求解对称锥线性规划(SCLP)的非单调光滑牛顿算法.通过应用欧氏若当代数理论,在适当的假设下,证明了该算法是全局收敛和超线性收敛的.数值结果表明了算法的有效性.

Bused on a modified version of the Chen-Harker-Kanzow-Smale （CHKS） smoothing function, this paper investigates a non-monotone smoothing Newton algorithm with a scaled central path for solving linear programming over symmetric cones （SCLP）. By using the theory of Euclidean Jordan algebras, we show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. Some preliminary numerical results is shown that our algorithm proposed is promising.