Sentence examples for minimizing sequence of from inspiring English sources

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).

If it is possible to verify that a minimizing sequence of (m_{infty}) is radially symmetric, the minimizer may be easily obtained.

A sequence is called a minimizing sequence of τ if.

Let ({u_{n}}) be a minimizing sequence of (I_{lambda}).

Indeed let { w n } be another minimizing sequence of τ.

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.

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.

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.

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 )