Sentence examples for a solution of the minimization from inspiring English sources

Therefore, x ∗ is a solution of the minimization problem (1.1).

Let x ∗ be a solution of the minimization problem (10).

Next, we introduce an explicit algorithm for finding a solution of the minimization problem (1.1).

Then { x n } n = 0 ∞ converges weakly to a solution of the minimization problem (1.1).

In particular, if f = 0, then the sequence { x n } converges strongly to a solution of the minimization problem (1.1).

We will show that the net { x t } defined by (3.1) converges to a solution of the minimization problem (1.1).

In 1976, Rockafellar [16] generally studied, by the PPA, the convergence to a solution of the convex minimization problem in the framework of Hilbert spaces.

If for all, where is a function, then the problem (1.1) becomes a problem of finding which is a solution of the following minimization problem: (1.3).

The optimality condition for (x^in S_{0}) to be a solution of the hierarchical minimization (5.4) is the variational inequality x^in S_{0},quad bigllangle nablapsi_{1} bigl(x^bigr),x-x^bigrrangle ge0,quad xin S_{0}.

The optimality condition for (x^in S_{0}) to be a solution of the hierarchical minimization (4.4) is the VI: x^in S_{0},quad bigllangle nablavarphi_{1}bigl(x^ bigr),x-x^bigrrangle ge0,quad xin S_{0}.

In order to jointly equalize diagonal terms of M k, we can choose θ such that it is a solution of the following minimization problem: θ = arg min ϕ ∑ k = 0 K − 1 | [ R a b T M k R a b ] a a − [ R a b T M k R a b ] b b | 2, (11).