A feasible conjugate-direction method to solve linearly constrained minimization problems

An iterative procedure is presented which uses conjugate directions to minimize a nonlinear function subject to linear inequality constraints. The method (i) converges to a stationary point assuming only first-order differentiability, (ii) has ann-q step superlinear or quadratic rate of convergence with stronger assumptions (n is the number of variables,q is the number of constraints which are binding at the optimum), (iii) requires the computation of only the objective function and its first derivatives, and (iv) is experimentally competitive with well-known methods.For helpful suggestions, the author is much indebted to C. R. Glassey and K. Ritter.This research has been partially supported by the National Research Council of Canada under Grants Nos. A8189 and C1234.