论文标题
通过半植物牛顿方法重新重新制定了M-STATATION条件作为不连续方程的系统及其解决方案
Reformulation of the M-stationarity conditions as a system of discontinuous equations and its solution by a semismooth Newton method
论文作者
论文摘要
我们表明，与具有互补性约束（MPCC）的数学程序相关的Mordukhovich-Stationarity系统可以等效地写成不连续方程的系统，可以使用半齿牛顿方法来解决。我们表明，所得算法可以解释为MPCC的主动集策略。该方法的局部快速收敛可以保证在MPCC卫星版本的LICQ和合适的二阶条件的有效性下保证。如果是线性季度MPCC，则可以用较弱的条件代替LICQ-Type约束资格，该条件取决于基础乘数。我们讨论适合我们方法的全球化策略。为了说明我们的理论发现，提出了一些数值结果。
We show that the Mordukhovich-stationarity system associated with a mathematical program with complementarity constraints (MPCC) can be equivalently written as a system of discontinuous equations which can be tackled with a semismooth Newton method. We show that the resulting algorithm can be interpreted as an active set strategy for MPCCs. Local fast convergence of the method is guaranteed under validity of an MPCC-tailored version of LICQ and a suitable second-order condition. In case of linear-quadratic MPCCs, the LICQ-type constraint qualification can be replaced by a weaker condition which depends on the underlying multipliers. We discuss a suitable globalization strategy for our method. Some numerical results are presented in order to illustrate our theoretical findings.
