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Therefore, [u.sup.*] is a minimizer of the functional [J.sub.[alpha]](u) and the proof is completed.
To mitigate the effect of these words, the speaker should use some minimizers. For instance (Leprocy and cancer, ....
Thus, if [[x.sup.*.sub.[phi]] is a minimizer of the objective (15) and all values [[a.sup.i.sub.[phi]] are not its minimizers then both subsets [Q.sub.-] and [Q.sub.+] are nonempty.
In this section, we will show that if ([[sigma].sup.(k)], [[delta].sup.(k)] [[epsilon].sup.(k)]) is a local minimizer of problem ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) and the parameter [[eta].sup.(k)] is sufficiently large as k [right arrow] [infinity], then [e.sup.(k)] [right arrow] [e.sup.*] = 0 and ([[sigma].sup.(k)], [[delta].sup.(k)]) [right arrow] ([[sigma].sup.*], [[delta].sup.*]) with ([[sigma].sup.*], [8.sup.*]) being a local minimizer of problem (P).
This paper presents a method to find global minimizer of the following 8th order polynomial minimization problem
This change designates the role of the surface energy at the minimizer u as a "counter" because [1/2][[integral].sub.0.sup.K] |[[partial derivative].sub.yy]u|dy counts the number of discontinuities in [[partial derivative].sub.y]u, where [[partial derivative].sub.y] u [member of] {[+ or -]1}.
Our first objective in this paper was to use the model to generate such predictions for three migration strategies: (1) early arrival at the breeding grounds (time minimizer), (2) arrival with excess energy reserves (energy maximizer), and (3) random (no strategy).
It was shown that the proposed iterative method converges towards a minimizer of the Tikhonov functional under consideration.
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