Sentence examples for be reformulated as finding from inspiring English sources

The original problem can now be reformulated as finding w = ( x, y ) ∈ S with G w = 0, or, more generally, minimizing the function ∥ G w ∥ over w ∈ S. Therefore solving SEP (1.1) is equivalent to solving the following minimization problem: min w ∈ S f ( w ) = 1 2 ∥ G w ∥ 2, (2.1).

The original problem can now be reformulated as finding w = ( x, y ) ∈ S with G w = 0, or, more generally, minimizing the function ∥ G w ∥ over w ∈ S. Algorithm 3.1 For an arbitrary initial point w 0== ( x 0, y 0 ), sequence { w n = ( x n, y n ) } is generated by the iteration: w n + 1 = α n ( I − γ G ∗ G ) w n + ( 1 − α n ) v n, v n ∈ R i ( n ) ( w n − γ G ∗ G w n ), (3.1).

Then our all pairs similarity search problem is reformulated as finding pairs such that f + g o γ o + g e γ e ≤ d.

which can be reformulated as, N A & B N A + N C − N A & C C ) > N A & C N A + N B − N A & B B ), (11).

Many problems in nonlinear analysis can be reformulated as a problem of finding a fixed point of a nonexpansive mapping.

Let X be a uniformly convex and smooth Banach space and let { x n } and { y n } be two sequences of X such that { x n } and { y n } is bounded, if ϕ ( x n, y n ) → 0, then ∥ x n − y n ∥ → 0. Many problems in nonlinear analysis can be reformulated as a problem of finding a fixed point of a nonexpansive mapping.

Let Π D be the generalized projection from a smooth, reflexive, and strictly convex Banach space X onto a nonempty closed convex subset D of X, then Π D is closed and quasi-ϕ-nonexpansive from X onto D. Many problems in nonlinear analysis can be reformulated as a problem of finding a fixed point of a nonexpansive mapping.

The linear complementarity problems (3.1) can be reformulated as the following variational inequality problems of finding (u_{alpha}^{ k)}in K), (alpha=1,-1), resuchthatly, such that bigl(A^{ k)}bigl u_{alpha}^{ k)}-u_{alpha}^{ k-1)} bigr)+rbigl(u_{ k-1a }^{(k-1)}bigr),v_{alpha}-u_{alpha}^{(k)} bigr)geq0,quad forall v_{alpha}in K, where ((v,w)=v^{T}w).

The classical direction finding problem can be reformulated as a sparse representation problem.

The minimization of can be reformulated as.

system (1.1) can be reformulated as (2.7).