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This is achieved by functional minimization of total irreversibility using the attractor trajectory optimization approach developed in the first part of this study.
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In the past, both parametric and functional minimizations of engine irreversibility have been studied extensively.
The problem of functional minimization is reduced to construction of a sequence of smooth nonlinear programming problems by introducing the auxiliary variables and applying the augmented Lagrangian method.
And then this turns the problem of object segmentation into the problem of energy functional minimization.
Fig. 2 a shows binding (adsorption) free energies (in kB T units) as a function of membrane-macroion separation from our model and as derived from the free-energy functional minimization scheme implemented by May et al. (20).
The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems.
For the functional minimization we use the quasi-Newton method of linear search.
Firstly, the minimizer, which is obtained by the minimization of energy functional (14), may become a local minimizer during curve evolution.
That is to say, the contours of the objects can be obtained by the minimization of energy functional (14) concerning level set function.
In [5], You and Kaveh proposed a class of fourth-order PDEs that are obtained by the minimization of a functional given as an increasing function of the edge detector Δu.
These rehabilitative interventions optimize surgical outcomes by reducing pain, improving strength and function and by minimization of complications.
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