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Gradient-based methods

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As its name means, gradient-based methods need the gradient of objective functions to design variables. The evaluation of gradient can be achieved by [[finite difference method, linearized method or adjoint method]]. Both finite difference method and linearized method has a time-cost proportional to the number of design variables and not suitable for design optimization with a large number of design variables. Apart from that, finite difference method has a notorious disadvantage of subtraction cancellation and is not recommended for practical design application.
 
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Suppose a cost function $J$ is defined as follows,
 
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<math>J=J(U(\alpha),\alpha)</math>
 
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where $U$ and $\alpha$
 
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Finite difference method:
 
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Linearized method:
 
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Adjoint method:
 

Latest revision as of 01:33, 6 January 2012

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