Development and Evaluation of a Primal-Dual Method for the Solution of Non-Linear Programming Problems with Linear Constraints.
NAVY PERSONNEL RESEARCH AND DEVELOPMENT CENTER SAN DIEGO CALIF
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A general algorithm for solving the class of nonlinear programming problems that have linear constraints has been developed. The constraints can be either equations or inequalities and the variables can be free or non-negative. The objective function is assumed to be continuously differentiable. The algorithm is an effective second-order method in that slow convergence is eliminated without requiring second partial derivations. It combines the desirable features of projection methods, conjugate gradient methods, and methods that solve LP problems to obtain feasible directions. Computational results on a wide variety of test problems are given. The comparison of two nonlinear programming algorithms--the primal-dual and the ricochet gradient--was employed as the vehicle for evaluating practices and standards employed in testing algorithms.
- Operations Research