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A point is said to be an efficient point of (VD) if (6.3).
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Conversely, Since is an efficient point of (VD), then.
By Theorem 6.4, we know that is an efficient point of (VD).
Then, and if and only if is an efficient point of (VD).
Lemma 2.1 x 0 is an efficient point for (MOP) if and only if x 0 solves ( M O P k ( x 0 ) ) Minimize f k ( x ) + s ( x | D k ) s u b j e c t t o f i ( x ) + s ( x | D i ) ≦ f i ( x 0 ) + s ( x 0 | D i ), f o r a l l i ≠ k, g j ( x ) ≦ 0, j = 1, ⋯, q. for every k = 1,..., p. We introduce the following definition for (MOP) based on the idea of Chandra et al. [19].
Still, anyone curious about the new Gershwin scholarship will find this book to be an efficient starting point for further exploration.
A point (yin D) is called an efficient point if ((D -y cap -C) = {0}) and a weak efficient point if ((D-y cap (-operatorname{int} C) =emptyset).
"The brain appears to be an efficient superhighway that gets you from Point A to Point B" when it comes to intelligence, Dr. Jung explained.
Based upon these generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution.
It could possibly be an efficient therapy target at this time point.
(overline{y}in M) is called a super efficient point of M if for any given (Vin N 0)), there exists (Uin N 0)) such that operatorname{cl} bigl operatorname{cone} M-overline{y}) bigr)cap (U-K) subseteq V, and we denote it by (overline{y} M-overline{y}
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

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