Optimization problems with a single variable have special importance in optimization theory. The reason for this is that multidimensional optimization problems are usually solved iteratively through optimization algorithms that utilize single variable optimization approaches. Typically, at the kth iteration of an algorithm, a promising search direction s(k) 2 <n in the n-dimensional parameter space is first determined. Starting from the solution at the kth iteration x(k), a line search is carried out in the direction s(k). A general point along that line is given by x 1/4 x(k) þ as(k), where a > 0 is the search parameter. The optimal value of the search parameter is the one that minimizes the objective function.
One-dimensional optimization-line search, Page 1 of 2
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