Sentence examples for no explicit solution from inspiring English sources

For more complex models, and in particular when there is no explicit solution, it is nearly impossible to establish theoretical conditions on the existence and uniqueness of the MLEs.

It is worth pointing out that if P is the zero matrix, then the iterative scheme (13) reduces to the conventional alternative direction method of multipliers (ADMM) for the constrained optimization problem (12) (see, e.g., [26]); in this case, the u-subproblem in (13) has no explicit solution and must be solved by an appropriate iterative algorithm, for example, FISTA in [7].

There is no explicit solution for K = E(g x ) so that an explicit expression for c n cannot be derived.

It is especially useful in the case of non-linear algebraic systems which have no explicit solution or have multiple or unstable solutions.

There is no explicit solution to (2), but the first order conditions, together with the boundary conditions that b i (c ¯ ; N ) = c ¯ for all i uniquely characterize optimal bidding strategies.

When k>1, the equations have no explicit solutions.

Most of nonlinear differential equations have no explicit solutions which are expressible in finite terms; even if a solution can be found, it is often too complicated to display clearly the principal featrues of the solution.

$$\end{document} Because there is no explicit inverse of the function f, we cannot obtain an explicit solution M t) of (5), but numerically the inverse can be obtained very easily.

We find an explicit solution to the problem posed by all these conditions.

Therefore, an explicit solution of (1) is obtained as follows: M ˜ n = − b n + 1 ( 0 ).

Moreover, an explicit solution for the considered problem has been provided.