互补问题的一个新的光滑乘子价值函数

New smooth multiplier merit function for complementarity problems

研究互补问题的新解法,给出了互补问题的一个新的光滑乘子价值函数,分析了乘子价值函数的性质,并构造了相应的算法。选取了新的下降方向和乘子修正方法,使价值函数获得两次下降,从而加快了下降速度。研究结果表明:在函数为一致P的条件下,算法具有全局收敛性、局部超线性收敛性和二次收敛性;对线性互补问题有限步收敛。

This paper introduces a new method aimed at complementarity problem and proposes a new smooth multiplier merit function. The paper offers an analysis of the property of the new smooth multiplier merit function and the construction of corresponding algorithm, which relies on the new descent direction and multiplier modified method, and the acceleration of descent of the algorithm due to merit function obtained twice. The new method shows global convergence, local superlinear convergence and quadratic convergence obtained under the assumption that F is a uniform P function. The method allows for finite termination of the algorithm for linear complementarity problems.