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.
- Variable scaling by the Variable Metric Method
- Use of conjugated search directions by the 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 [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
- ↑ J. Arora, Introduction to Optimum Design, Elsevier, second edition, 2004
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