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(3) Functional Verification: As opposed to the first two objectives, functional verification is concerned with the question whether or not an implementation behaves according to the behavioral specifications of the system.
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The piecewise constant M-S model is a very useful simplified version of the M-S functional (1), in which the objective functional is minimized over functions that take a finite number of values.
In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient.
We design an algorithm to update the shape and the impedance function alternatively along the descent direction of the objective functional.
The objective functional is given by (1.2).
An iteration scheme is developed to solve the objective functional.
For this purpose, we design the objective functional J.
On the Banach space, and the associated objective functional (1.4).
Next, the topological derivative of the objective functional is derived.
In many control problems, the objective functional contains the gradient of the state variables.
The integrand of the objective functional is convex on Θ. 5.
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