一类等式约束非线性优化问题的序列二次规划新方法

A New Sequential Quadratic Programming Method for Nonlinear Equality-Constrained Optimization

本文提出一类新的序列二次规划方法来求解等式约束的非线性优化问题,方法不使用罚函数,避开了罚因子的选取对数值结果的影响,也不采用滤子技巧,去除了滤子方法中的恢复过程。在两个温和条件的假设下,步长的选取不需要目标函数和约束违反度的充分下降,扩大了算法的适用范围,证明了算法的全局收敛性。使用Matlab软件,编写了算法的程序,进行了数值试验,并与著名的优化软件LANCELOT比较,结果表明算法强健有效。

This paper presented a new sequence quadratic programming method for solving nonlinear equality constrained optimiza- tion problems. The new method did not use the penalty function, avoided the selection of penalty factor for the numerical results, and also did not use filter tips, removing the filter method in the recovery process. In two mild conditions under the assumption, step size did not need the objective function and the constraint violation for the sufficient descent, expanding the scope of application of the algorithm, the global convergence was proved. Using Matlab software, the preparation of the algorithm procedures, numeri- cal experiments are carried out, and compared with the well-known optimization software LANCELOT, the results show that the algorithm is robust and effective.