Two numerically stable algorithms are presented for the solution of unconstrained optimization problems. These algorithms have clearly defined advantages over alternative methods and the class of problems on which they should be used in preference to other algorithms is identified. The generalization of the algorithms to the linearly constrained problem handles constraints in an identical manner to that given for linear programming and quadractic programming. The formulation of various basic factorizations is considered and how these are modified from iteration to iteration, discussed. These factorizations could be implemented into both existing algorithms for linearly constrained optimization problems and any new algorithm that may arise. (Author)
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