QUASI-NEWTON METHOD FOR MINIMIZATION UNDER LINEAR CONSTRAINTS WITHOUT EVALUATING ANY DERIVATIVES

In this paper a method is described for solving linearly constrained nonlinear programming problems without evaluating any derivatives of the objective function. The algorithm uses the concept of active constraints and avoids the calculation of derivatives by approximating modified gradients and Hessian matrices by the aid of differences of function values. These approximations are calculated in such a way that the same convergence results are obtained as for any Quasi-Newton method. © 1979 Springer-Verlag.