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A method for the minimization of a function of several variables. It is based on the fact that each successive approximation of the function  $  F $
is obtained from the preceding one by a shift in the direction of the gradient of the function:

$$ 
\mathbf x ^ {n + 1 }  = \ 
\mathbf x  ^ {n} - \delta _ {n} \ 
 \mathop{\rm grad}  F ( \mathbf x  ^ {n} ).
$$

The parameter  $  \delta _ {n} $
can be obtained, e.g., from the condition of the magnitude

$$ 
F ( \mathbf x  ^ {n} - \delta _ {n} \ 
 \mathop{\rm grad}  F ( \mathbf x  ^ {n} )) \ \ 
\textrm{ being  minimal  } .
$$

See also [[Descent, method of|Descent, method of]]; [[Steepest descent, method of|Steepest descent, method of]].

====Comments====

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.E. Dennis,   R.B. Schnabel,   "Numerical methods for unconstrained optimization and nonlinear equations" , Prentice-Hall  (1983)  {{MR|0702023}} {{ZBL|0579.65058}} </TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  R. Fletcher,   "Practical methods of optimization" , Wiley  (1980)  {{MR|0585160}} {{MR|0633058}} {{ZBL|0439.93001}} </TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  D.G. Luenberger,   "Linear and nonlinear programming" , Addison-Wesley  (1984)  {{MR|2423726}} {{MR|2012832}} {{ZBL|0571.90051}} </TD></TR></table>