非线性规划问题的一个全局收敛的次可行方向法

本文给出非线性不等式约束最优化问题的一个初始点可行取的算法，利用梯度投影构造搜索方向，并使用符号函数对搜索方向和搜索函数进行有效的控制，使得一旦迭代点进入了可行域，其后的方向将成为可行下降方向，搜索函数将由罚函数变为原问题的目标函数（故称之为次可行方向法）在较为温和的条件下证明了方法的全局收敛性，及罚参数只需进行有限次调整。

A GLOBAL CONVERGENT SUBFEASIBLE DIRECTION METHOD FOR NONLINEAR PROGRAMMING PROBLEMS

This paper presents an algorithm for nonlinear inequality constrained optimization problems which begins at any starting point.The search direction is formed by using gradient projection, and the search directions and functions are controlled effectively by the sign functions. Such that the direction will become feasible descent direction, and the search function will change into the objection function from penalty function whenever some iteration point go into the feasible region. (So call it subfeasible direction method.) It is shown that this method possesses global convergence and the penalty parameters are adjusted only finite times under mild conditions.