Sentence examples for minimizing sequences of from inspiring English sources

By constructing approximating minimizing sequences of functions twice, we also obtained the optimal controls of impulsive fractional differential equations.

By constructing approximating minimizing sequences of functions, the existence of optimal controls of systems governed by nonlinear impulsive evolution equations is also presented.

Constructing approximating minimizing sequences of functions twice plays a key role in the proof of looking for optimal controls, which enable us to deal with the multiple solution problem of feasible pairs.

Due to the lack of uniqueness of feasible pairs, we mainly apply the idea of constructing approximating minimizing sequences of functions twice and derive the existence of optimal controls.

The proof again consists of testing the functional on minimizing sequences of the form (eta U_epsilon ), where (U_epsilon ) is an extremal for (mu _{gamma, s}(mathbb {R}^n)) and (eta in C^infty _c(Omega )) is a cut-off function equal to 1 in a neigbourhood of 0, and showing that (mu _{gamma,s, lambda }(Omega )

We then propose a penalization technique to recover the minimizing sequences of the original problem from the optimal solution of the relaxed one.

This fact together with Lemma 2.7 implies that a type I (resp., type II) LP minimizing sequence of (P) is a type I (resp., type II) LP approximating solution sequence.

(i) Similar to the proof of Lemma 2.7, it is also routine to check that a sequence is a generalized type I (resp., generalized type II) LP approximating solution sequence if and only if it is a generalized type I (resp., generalized type II) LP minimizing sequence of (P).

Firstly, we provide the existence of minimizing sequences for J λ on M λ and M λ − as λ is sufficiently small.

Prior to sequencing we included amplification of the inserts of recombinant clones directly from the colonies with primers SD2 and SA4 as a preselection step to minimize sequencing of small exon trapping products.

In case there is no minimizer, we determine the asymptotic behavior of minimizing sequences.