We use spectral projected gradient (SPG) method to seek for the minimizers of the constraint functional and prove the convergence.
In Section 4, the spectral projected gradient method is applied to compute the minimizers. Section 5 provides a detailed exposition of multiparameter choice rule based on the balancing principle.
To mitigate the effect of these words, the speaker should use some minimizers. For instance (Leprocy and cancer, ....
Expression of admiration is accompanied by minimizers which causes protection from bad or evil eyes.
Let X be a set of all minimizers of the objective function (15) and [A.sub.[phi]] = ([a.sup.1.sub.[phi]], ..., [a.sup.m.sub.[phi]]) be the set of angular coordinates of the existingfacilities (demand points).
Thus, if [Q.sub.+] = 0 then [x*.sub.[phi]] is not a minimizer of the objective function (15) unless all values [a.sup.i.sub.[phi]] are its minimizers.
The problem whether such functionals yield regularizations of the underlying inverse problem (i.e., whether minimizers of (1.3) converge to a solution of (1.1) as [alpha], [delta] [right arrow] 0) has been analyzed intensively for linear and nonlinear settings over the last years; see, e.g., [12, 20, 24, 32, 37].
Furthermore, the sequence of minimizers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] should converge to a minimizer of problem (3.1).
The result is an apparently robust method for approximating what are usually difficult minimizers
By definition, time minimizers
will have higher reproductive success if they arrive early in the window, and energy maximizers will have higher reproduction if they arrive with extra energy reserves.
The paper  provides classical results on the existence of minimizers
, stability, and convergence for the particular approach considered here using Tikhonov regularization.
One hope is that the minimizers
for Tikhonov regularization with penalty term [[PSI].sub.p[beta]][(x).sup.p] are not that far away from the minimizers
of Tikhonov regularization with penalty [[PSI].sub.p[beta]](x) and that they have similar sparsity patterns.