Users:Structural Optimization/Optimization Algorithms/Steepest Descent

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Contents

Motivation

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

sk = -∇ fk.

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.

The method of steepest descent can be extended to the Constraint Steepest Descent (CSD) method which is applicable to constrained optimization problems [1].

Input Parameters

Block headline
Parameter Values, Default(*) Description
OPT-CTR int : STEEP_DESC_NAND ID and identifier of optimization algorithm.
Common Compulsory Parameters, valid for all optimization algorithms
FILTER OPT-FILTER int, int, .... One or more filter function IDs.
OBJ OPT-RESPONSE_FCT int, int, ... One or more response functions that are considered as objective.
OUTPUT PC-OUT int The Output object.
DOMAIN EL-DOMAIN int The respective domain on which the optimization problem is defined.
REGULARIZATION EL-REGULARIZATION int The regularization object.
LINE_SEARCH OPT-LINE_SEARCH int The line search object.
CONVERGENCE_CONTROL OPT-CONVERGENCE int The convergence checker.
Common Optional Parameters, valid for all optimization algorithms
DESIGN_SPACE_BOUNDS ND-SET int, int, ... One or more node set IDs that define the boundary of the design space.
RESTART_DATA_FREQ int Frequency of restart output,


Input Example

Example of a complete input block:

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

References

  1. J. Arora, Introduction to Optimum Design, Elsevier, second edition, 2004




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