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Computational Algorithm for Unconstrained Minimization.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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A generalized descent algorithm theory is developed for unconstrained minimization problems. Here a descent algorithm is defined as a computational procedure where at each iteration a descent direction is determined and a single dimensional search is made for the minimum in the descent direction. The theory is shown to be a generalization of the three most common descent algorithms gradient, conjugate gradient and Fletcher-Powell. Since execution of the single dimensional search can be computationally time consuming, two additional algorithms are presented which reduce or eliminate single dimensional search time. The first is a modification of Davidons Variance Algorithm and requires a minimal single dimensional search. The second is a direct method for minimizing a special class of quadratic functions. Author
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