In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear semideflnite programming. At each iteration, two systems of linear equations with the same coefficient matrix are solved to determine search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for traditional filter methods. The proposed algorithm is globally convergent under some mild conditions. Preliminary numerical results indicate that the proposed algorithm is comparable.

中文翻译：

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一种无惩罚函数或非线性半定规划滤波器的无 QP 新算法

在本文中，我们提出了一种无惩罚函数或非线性半定规划滤波器的无 QP 算法。在每次迭代中，求解具有相同系数矩阵的两个线性方程组以确定搜索方向；非单调线搜索确保目标函数或约束违反函数被充分减少。我们的算法中没有可行性恢复阶段，这是传统过滤方法所必需的。所提出的算法在一些温和的条件下是全局收敛的。初步的数值结果表明所提出的算法具有可比性。