|
| 摘要: |
| 本文针对非线性规划一些经典的算法一般不能直接应用到均衡问题上来的缺点,利用一个互补函数以及光滑近似法的思想,把非线性互补约束均衡问题转化为一光滑非线性规划问题,该光滑非线性规划问题通过一个新的QP-free算法求解.特别地,在不要求Hessian阵估计正定的假设条件,算法仍具有全局收敛性.且在一些适当的假设条件下,得到了超线性收敛速度.数值实验结果表明本文提出的算法是可行的. |
| 关键词: 均衡问题 非线性互补 QP-free算法 全局收敛性 超线性收敛性 |
| DOI： |
| 分类号:O221.2 |
| 基金项目:国家自然科学基金(11061011,11361018)、广西杰出青年S金(2012GXSFFA060003)、河南省教育厅科学技术研究重点项目(12B110011). |
|
| A new QP-free algorithm for mathematical programs with nonlinear complementarity constraints |
|
Fenghua Chen,Shuangan Li
|
| Abstract: |
| Against the shortcomings that many existing algorithms for solving the standard smoothing nonlinear programming would fail if they were used directly to solve the mathematical programs with equilibrium constraints (MPEC). By using a complementarity function and the idea of smoothing approximation method, the mathematical program with equilibrium constraints (MPEC) problem was transformed into a nonlinear programming, and a QP-free algorithm is proposed for the solution of (MPEC) problem. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergent. And superlinear convergence is obtained under some suitable assumptions. Numerical experiment results show that the proposed algorithm is feasible. |
| Key words: Program with equilibrium constraints Nonlinear complementarity QP-free algorithm global convergence superlinear convergence |
