A Primal-Dual Method for Minimization with Linear Constraints
NAVAL PERSONNEL AND TRAINING RESEARCH LAB SAN DIEGO CA
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The purpose of the report is to develop a general algorithm for solving the class of nonlinear programming problems that have linear constraints. 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 derivatives. In addition 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. Some comments on the efficiency of the algorithm as compared to other algorithms is included.
- Operations Research