CAJ | 학술논문

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。
위료획득서렬이차규화방법적전국수렴성，통상수요차조일개벌함수，단상용적벌함수유우구유불가미성종이급계산대래일정적곤난，랍격랑일함수수연가이극복차곤난，단기형식교위복잡，위해결해문제，급출료일류광활화벌함수。기우일류쌍곡여현형광활화벌함수，제출료등식약속우화문제적일개광활화서렬이차규화방법。해광활화함수구유량호적련속、가미성화철성질，재괄당조건하，획득료산법적전국수렴성，병급출수치측시설명료산법적유효성。
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.