A class of descent algorithms for nonlinear function minimization with linear equality constraints

Abstract

We consider the application of the ABS algorithms, introduced by [I], mainly for the solution of linear algebraic systems, to constrained optimization problems with equality constraints. A general formulation of feasible direction algorithms is obtained and the ABS formulation is given of the reduced gradient method of Wolfe (1967) and of the projected gradient method of Rosen (1960)