不等式约束最优化超线性与二次收敛的强次可行SQP算法

利用ＳＱＰ方法、广义投影技术和强次可行方（向）法思想,建立不等式约束优化一个新的初始点任意的快速收敛算法． 算法每次迭代仅需解一个总存在可行解的二次子规划,或用广义投影计算“一阶”强次可行下降辅助搜索方向;采用曲线搜索与直线搜索相结合的方法产生步长． 在较温和的条件下,算法具有全局收敛性、强收敛性、超线性与二次收敛性． 给出了算法有效的数值试验．

A Superlinearly and Quadratically Convergent SQP Algorithm For Inequality Constrained Optimization

Using the SQP method, the generalized projection technique and the idea of strongly subfeasible direction method, this paper presents a new fast convergent algorithm with arbitrary starting point for inequality constrained optimization. At each iteraion, the algorithm solves only one quadratical programming, or uses the generalized projection to compute a "first-order" strongly subfeasible descent auxiliary search direction; it utilizes a curve search and a straight search to yield the step size. Under milder hypotheses, the algorithm possesses global and strong convergence, superlinear and quadratical convergence. Some effective numerical tests are done.