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[[Category: Users:Structural Optimization]]

== Motivation ==

The most simple unconstrained optimization algorithm is the method of Steepest Descent (SD). It computes the search direction at step ''k'' by 

'''s'''<sup>''k''</sup> = -∇ f<sup>''k''</sup>. 

Thus, it is always ensured that the objective can be improved. The basic drawback of the SD method is bad convergence if the magnitudes of design variables differ seriously. This ends up in the well known zigzagging behavior and slow convergence rate. There exist two efficient approaches to improve the convergence behavior.
*Variable scaling by the Variable Metric Method
*Use of conjugated search directions by the [[Users:Structural Optimization/Optimization Algorithms/Conjugate Gradient | Conjugate Gradient Method]].
The method of steepest descent can be extended to the Constraint Steepest Descent (CSD) method which is applicable to constrained optimization problems <ref name="Textbook by J. Arora"> J. Arora, Introduction to Optimum Design, Elsevier, second edition, 2004 </ref>.

== Input Parameters ==

{| border="1" cellpadding="3" cellspacing="0"
|colspan="3" style="background:#efefef;"| Block headline
|-
!Parameter
!Values, Default(*)
!Description
|-
!     OPT-CTR      
|''int'' : STEEP_DESC_NAND
|ID and identifier of optimization algorithm.
|-
{{Users:Structural Optimization/Optimization Algorithms/Common Parameters}}
|}


=== Input Example ===

Example of a complete input block:
<pre>
OPT-CTR 1 : STEEP_DESC_NAND
  ! compulsory parameter
  FILTER=OPT-FILTER 1
  OBJ=OPT-RESPONSE_FCT 1
  OUTPUT=PC-OUT 1
  DOMAIN = EL-DOMAIN 1
  REGULARIZATION = EL-REGULARIZATION 1
  LINE_SEARCH = OPT-LINE_SEARCH 1
  CONVERGENCE_CONTROL = OPT-CONVERGENCE 1
  ! optional parameter
  DESIGN_SPACE_BOUNDS = ND-SET 6
</pre>

== References ==

<references/>