一种新的求解圆锥规划的非内点算法

A new non-interior point algorithm for circular cone programming

摘要:

针对一般的圆锥优化问题，本文提出了一种新的非内点算法.改算法根据圆锥与二阶锥的关系通过引入一个与圆锥规划互补条件等价的投影方程将问题转化为线性方程组求解，且在每步迭代中只需求解一个系数矩阵固定的线性方程组并执行两次投影运算.该算法还具有可以从任意初始点开始且不要求仿射约束系数矩阵的行向量组线性独立等特点.本文还在较弱的假设条件下证明了算法的全局收敛性.数值试验结果表明提出的算法快速有效.

Abstract:

A new non-interior point algorithm is proposed for solving the circular cone programming (CCP). Based on the relationship between the circular cone and the second-order cone, a projection equation that is equivalent to the complementary condition of the CCP is introduced.Then the problem is transformed into a linear system of equations. The method only needs to solve the linear equations with the same coefficient matrix and compute two projections at each iteration. Moreover, the algorithm can start from an arbitrary point and does not require the row vectors of the affine constraint coefficient matrix to be linearly independent. Under weaker assumptions, the global convergence of the algorithm is proved. Numerical results show that the algorithm is fast and effective.