Namespaces
Variants
Actions

Difference between revisions of "Gradient method"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
m (MR/ZBL numbers added)
Line 13: Line 13:
  
 
====References====
 
====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)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  R. Fletcher,  "Practical methods of optimization" , Wiley  (1980)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  D.G. Luenberger,  "Linear and nonlinear programming" , Addison-Wesley  (1984)</TD></TR></table>
+
<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>

Revision as of 11:59, 27 September 2012

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

The parameter can be obtained, e.g., from the condition of the magnitude

See also Descent, method of; Steepest descent, method of.

Comments

References

[a1] J.E. Dennis, R.B. Schnabel, "Numerical methods for unconstrained optimization and nonlinear equations" , Prentice-Hall (1983) MR0702023 Zbl 0579.65058
[a2] R. Fletcher, "Practical methods of optimization" , Wiley (1980) MR0585160 MR0633058 Zbl 0439.93001
[a3] D.G. Luenberger, "Linear and nonlinear programming" , Addison-Wesley (1984) MR2423726 MR2012832 Zbl 0571.90051
How to Cite This Entry:
Gradient method. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gradient_method&oldid=13020