针对非线性不等式约束半定规划问题提出一种新的逐次线性化方法, 新算法既不要求罚函数单调下降, 也不使用过滤技巧, 尝试步的接受准则仅仅依赖于目标函数和约束违反度, 罚函数中对应于成功迭代点的罚因子不需要单调增加. 新算法或者要求违反约束度量有足够改善, 或者在约束违反度的一个合理范围内要求目标函数值充分下降, 在通常假设条件下, 分析了新算法的适定性及全局收敛性. 最后, 给出了非线性半定规划问题的数值试验结果, 结果表明了新算法的有效性.

A successive linearization method with flexible penalty is presented to solve a nonlinear semidefinite programming with nonlinear inequality constraints. The new method does not require the penalty function to be reduced and does not use filter technique. The storage of the filter set is avoided. The updating of the penalty parameter is flexible, which is only dependent on the message of the current iterate. The penalty parameter sequence corresponding to the successful iterate point does not need to increase monotonically. To decide whether the trial step can be accepted or not, the new method requires the measure of constraint violation to be improved or the value of the objective function to be improved within the measure of feasibility control. Under the usual assumptions, we prove that the algorithm is well defined and globally convergent. Finally, preliminary numerical results are reported.