Sentence examples for a strict minimizer of from inspiring English sources

Then x0is a strict minimizer of order m for (MOP).

Hence, x0 is a strict minimizer of order m for (MOP).

Then x̄ is a strict minimizer of order σ of with respect to ψ of (MP).

Hence, x ¯ is a strict minimizer of order m for (MOP).

Now, suppose that x 0 is not a strict minimizer of order m in (MOP).

Thereby implying that x0 is a strict minimizer of order m for (MOP).

Then x 0 is a strict minimizer of order m for (MOP).

Hence x̄ is a strict minimizer of order σ with respect to ψ for (MP).

If x 0 is a strict minimizer of order m with respect to a nonlinear function ψ, then it is also a strict minimizer of order j with respect to the same ψ for all j > m.

If conditions (1 -(4) are satisfied, then x̄ is a strict minimizer of order σ of (MP).

A point x 0 ∈ S is a local strict minimizer of order m for (MOP) with respect to a nonlinear function ψ : S × S → R n, if there exists an ε > 0 and a constant c ∈ int R + p such that f ( x ) ≮ f ( x 0 ) + c ∥ ψ ( x, x 0 ) ∥ m for all  x ∈ B ( x 0, ε ) ∩ S. Definition 2.4 Let m ≥ 1 be an integer.