Sentence examples for derived necessary from inspiring English sources

Moreover, Ward [5] derived necessary and sufficient conditions for strict minimizer of order m in nondifferentiable scalar programs.

Subsequently, Bonnel [8] derived necessary optimality conditions for the semivectorial bilevel optimization problem in very general Banach spaces.

Chuong et al. [10] derived necessary and sufficient conditions for lower and upper semi-continuity of Pareto solution maps for parametric semi-infinite multiobjective optimization problems.

Chuong and Yao [12] derived necessary and sufficient optimality conditions of strongly isolated solutions and positively properly efficient solutions for nonsmooth semi-infinite multiobjective optimization problems.

Keeping this point of view, Yuan et al. [13] introduced locally ( H p, r, α ) -preinvex functions and locally H p -invex sets and derived necessary and sufficient optimality conditions for nonlinear programming problems.

For a scalar optimization problem, Auslender [5] derived necessary and sufficient optimality conditions for isolated local minima of order 1 and 2, and Ward [6] presented the notion of strict local minimum of order m.

In this paper, we use generalized convex functions, in terms of the right upper-Dini-derivative to derive necessary and sufficient optimality conditions for a general minimax programming problem and duality results for its Mond-Weir type dual model.

Instead of regarding existence as a predicate (2 70 4), Kant derives necessary existence from possibility (2 77 84)[26] The bond governing nature is derivable from its intelligible possibility, and not from any anthropological story nor from the notion of a necessary being.

The following lemma is essential in deriving necessary optimality conditions.

We find sufficient conditions for continuity of the Weyl product and we derive necessary conditions.

To derive necessary optimality conditions one needs to impose some kind of constraint qualification.