Extrema the steepest-descent method

A large category of problems consists in finding the extremum of a function with respect to several variables. Finding the maximum of a function /(x) is equivalent to finding the minimum of —/(x), so the discussion will be restricted to the search for minima. Let us assume that /(x) is a function in the n variables xt,x2.x collected 

The scalar a, equation (3.2.20), is estimated by crude linear search, g is the convergence criterion given by equation (3.2.21). Values in italic refer to the minimum along the search direction. 

At the minimum along the kth search direction, the old and the new directions should be orthogonal, i.e., 

Calculate by the steepest-descent method the minimum of the function 

The solution is obviously (0, 0). The first four stages of linear search are given in Table 3.12.o 

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