Sentence examples for a constrained solution from inspiring English sources

This speed does come at the cost of a constrained solution.

Thus, the theoretical formulation simplifies into a non-linear extremal problem with a constrained solution due to a singularity which is solved analytically.

When comparing the nutrient limited cycles to the individual models (e.g. Alanine and Cori cycles), the multi-tissue simulation approach showed a constrained solution space.

Replacement cost has a mathematically clear definition (Cabeza & Moilanen, 2006), measured via the difference between an optimal unconstrained and optimal constrained solution.

Since (A ( theta ) ) is a fixed subspace of Y, then there forever is an algebraic operator part of A. Next, we introduce the concept of a constrained extremal solution of multi-valued linear inclusions in Banach spaces.

In particular, if (R ( T ) ) is closed in Y, then (L ( x ) =y) always has a constrained extremal solution with respect to S. (III) Assume that (3.12) and that (N ( T ) =N ( A ) cap N ( L ) ) is closed in X.

In Theorem 3.1, the three equivalent characterizations of a constrained extremal solution of the linear inclusion (yin L ( x ) ) with respect to S are expressed in terms of algebraic operator parts and the generalized orthogonal complement of (R ( A )).

(II) (L ( x ) =y) has a constrained extremal solution with respect to S if and only if L bigl(A^ ( z ) bigr -yin R ( T ) dotplus F_{Y}^{-1} bigr -yin T ) ^{bot} bigR).

We first establish three equivalent characterizations of a constrained extremal solution of linear inclusions in Banach spaces by means of the algebraic operator parts, the metric generalized inverse of multi-valued linear operator, and the dual mapping of the spaces.

Consequently, it follows from (3.3) and (3.4) that (win D ( L ) cap S) is a constrained extremal solution of the linear inclusion (yin L ( x ) ) with respect to S if and only if (w=g-k) for some (kin D ( L ) cap N) such that k is an extremal solution of (L_{S, P} ( g ) -yin A ( x )).

For any (winOmega_{y}), i.e. (win D ( L ) cap S) is a constrained extremal solution of the linear inclusion (yin L ( x ) ) with respect to S. By (1) ⇔ (2) in Theorem 3.1, we have (winOmega_{y}) if and only if (k:=g-win D ( L ) cap N) is an extremal solution of the linear inclusion (L_{S,P} ( g ) -yin A ( x )).