非线性规划中的投影变尺度算法

摘要

To solve nonlinear optimization with equality constraints or inequality constraints,an improved proj ect variable metric algorithm is proposed.Based on an active set strategy,the direction is combined with the descent direction,the feasi-ble direction and the revised direction.Part of the direction is combined with the feasible direction and the revised direction. In conditions that feasible sets are nonempty,the functions of problem are twice continuously differentiable,the vectors of constraints are linearly independent,global convergence and superlinear convergence of the proposed algorithm is proved.%利用投影变尺度算法，求解一类包含等式和不等式约束的一般非线性规划问题。算法基于积极集，将下降方向、可行方向、修正方向3个方向的合理组合作为算法搜索方向，且可行方向与修正方向仅需修改变尺度投影梯度方向中的部分分量。在可行集非空、问题函数2次连续可微、约束条件线性无关等条件下，证明了算法的全局收敛性和超线性收敛性。