非线性优化问题的光滑化序列二次规划方法

为了获得序列二次规划方法的全局收敛性,通常需要借助一个罚函数,但常用的罚函数由于具有不可微性从而给计算带来一定的困难,拉格朗日函数虽然可以克服此困难,但其形式较为复杂,为解决该问题,给出了一类光滑化罚函数.基于一类双曲余弦型光滑化罚函数,提出了等式约束优化问题的一个光滑化序列二次规划方法.该光滑化函数具有良好的连续、可微性和凸性质,在适当条件下,获得了算法的全局收敛性,并给出数值测试说明了算法的有效性.

Smoothing Sequence Quadratic Programming Method for Nonlinear Optimization

To obtain the global convergence in the sequence quadratic programming(SQP) method, one often uses a penalty function.Due to its non-differentiability, the general penalty function will cause some numerical difficulty.The Lagrange function can overcome this difficulty, but it is complex in form.In the paper, a kind of smoothing penalty functions was developed and a sequence quadratic programming algorithm for equality constrained optimization problems was proposed.The smoothing function is based on the cosh function and it is continous, diffientiable and convex.The global convergence was achieved under certain conditions.The numerical tests were also given to show the effectiveness of the proposed algorithm.