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.
-Suppose a cost function $J$ is defined as follows,
-<math>J=J(U(\alpha),\alpha)</math>
-where <math>$U$</math> and <math>$\alpha$</math>
-Finite difference method:
-Linearized method:
-Adjoint method:

Latest revision as of 01:33, 6 January 2012