Research On The Geometric Algorithms For Programs With Constraints Of Linear Equalities

In this paper we discuss the geometric algorithms for programs with constraints of linear equalities. It mainly consists of three parts.In the first part, by means of the geometric characterization of the distance from a point to a linear manifold, an algorithm for programs with positive definite Hesse matrix of the cost functions and constraints of linear equalities is presented. Compared with the Newton’s algorithm, the algorithm here avoids computation of the inverse of the Hesse matrix of the cost function and multiplication of matrices.In the second part, by means of the geometric characterization of the distance from a point to a linear manifold and BFGS update, an algorithm for programs with constraints of linear equalities is proposed. The convergence theorems are proved, and some numerical examples are given.In the third part, by means of the geometric characterization of the distance from a point to a linear manifold and generalized quasi-Newton update, an algorithm for programs with constraints of linear equalities is proposed. The convergence theorems are proved, too. Some numerical examples arc given to show the feasibility of the algorithm.