Sentence examples for a minimal solution from inspiring English sources

A minimal solution is the one that minimizes the summed changes of the 5 variables.

Although mathematical solutions for specific boundaries had been obtained through the years, it was not until 1931 that Douglas (and independently the Hungarian American mathematician Tibor Radó) first proved the existence of a minimal solution for any given "simple" boundary.

Although mathematical solutions for specific boundaries had been obtained through the years, it was not until 1931 that the American mathematician Jesse Douglas (and independently the Hungarian American mathematician Tibor Radó) first proved the existence of a minimal solution for any given "simple" boundary.

It is guaranteed that a minimal solution exist, consisting of prime compatibles only.

Only the element x ¯ = 0 is a minimal solution of ( SP − ⪯ C l ).

A minimal solution may be defined similarly by reversing the last inequality.

Further iterations are possible and this gives a convergent sequence of upper and lower bounds under the conditions of Theorems 5 and 6 and provided that Perron-Kreuser theorem holds (which implies that the recurrence admits a minimal solutions).

A point is called a weakly minimal solution of (GVOP) with respect to the cone, if is a weakly minimal point of (GVOP) with respect to the cone, that is,.

In order to avoid the convergence to a local minimal solution around an initial shape, the topological derivative is introduced.

A point is said to be a weakly minimal solution of if satisfying and.

Suppose that, and the following conditions are satisfied: (i), ; (ii) is -convex like on a nonempty convex subset ; (iii) is a weakly minimal solution of ; (iv) - fulfills the weak domination property for all and ; (v)There exists an such that.