An Algorithm for Linearly Constrained Nonlinear Programming Problems

摘要

In this paper an algorithm for solving a linearly constrained nonlinear programming problem is developed. Given a feasible point, a correction vector is computed by solving a least distance programming problem over a polyhedral cone defined in terms of the gradients of the 'almost' binding constraints. Mukai's approximate scheme for computing step sizes is generalized to handle the constraints. This scheme provides as estimate for the step size based on a quadratic approximation of the function. This estimate is used in conjunction with Armijo line search to calculate a new point. It is shown that each accumulation point is a Kuhn-Tucker point to a slight perturbation of the original problem. Furthermore, under suitable second order optimality conditions, it is shown that eventually only one trial is needed to compute the step size. (Author)