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Both problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using the material derivative method and the adjoint variable method.
The shape gradient function and the optimality conditions for this problem are derived theoretically using the material derivative method and the adjoint variable method.
The shape gradient function, the size gradient function, and the optimality conditions for this problem are theoretically derived with the Lagrange multiplier method, the material derivative method, and the adjoint variable method.
We derive the shape gradient function by using the material derivative method and apply it to the free-form optimization method for determining the optimal shape.
The 3 point derivative method is faster than Hamming-window parabolic filtration method, so we conclude that the 3 point derivative method is optimal for 3D FBP.
This work utilises a non-invasive strain derivative method to estimate the applied transverse shear force.
The pressure derivative method and analysis of middle-time test data are also analyzed.
We aim to introduce the Fourier-spectral derivative method into the Poincare maps method.
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Non-derivative method, no gradient information.
This non-derivative method provides the effective solution algorithm.
"For any non-derivative method, the issue of termination is problematical as well as highly sensitive to problem scaling.
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