This paper presents a new projected Barzilai–Borwein method for the complementarity problem over symmetric cone by applying the Barzilai–Borwein-like steplengths to the projected method. A new descent direction is employed and a non-monotone line search is used in the method in order to guarantee the global convergence. The projected Barzilai–Borwein method is proved to be globally convergent under some suitable conditions. Some preliminary computational results are also reported which confirm the good theoretical properties of the proposed method.

中文翻译：

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对称锥互补问题的新投影 Barzilai-Borwein 方法

本文通过将 Barzilai-Borwein-like 步长应用于投影方法，提出了一种新的投影 Barzilai-Borwein 方法，用于解决对称锥上的互补问题。该方法采用新的下降方向，并使用非单调线搜索，以保证全局收敛。证明了投影的 Barzilai-Borwein 方法在某些合适的条件下是全局收敛的。还报告了一些初步计算结果，这些结果证实了所提出方法的良好理论特性。