Improved Algorithm Of Wolfe For The Linear Constrained Nonlinear Programming Problem

In this paper, an improved algorithm of Wolfe for the constrained nonlinear programming problem is discussed and we offer a new way to research methods of nonlinear programming by that. First of all, on the base of the reduced gradient method of Wolfe, we added accurate one dimension searching method into it and gained a new algorithm (algorithm 1,2) for the nonlinear programming with linear equality constraints and quadratic programming problems, and proved convergence of algorithm, then, we use above algorithms into other nonlinear programming problems with equality constraints, such as: nonlinear programming problem with nonlinear equality constraints, nonlinear programming problems with mixed constraints, nonlinear multi-objective programming problem with linear equality constraints, nonlinear multi-objective programming problem with general equality constraints, and nonlinear multi-objective programming problem with mixed constraints. We set up series of improved algorithms with accurate one dimension searching method. Moreover a lot of numerical examples have been given for new algorithms, showed the new algorithms with accurate one dimension searching method are feasible and effective.