Sentence examples for established necessary from inspiring English sources

Further, Movahedian and Nobakhtian [9] established necessary optimality conditions for Lipschitz MPEC on Asplund space and sufficient optimality conditions for nonsmooth MPEC in Banach space.

They also established necessary optimality theorems for robust efficient solutions and gave scalarization methods for robust efficient solutions of multiobjective optimization problems.

Subsequently, Kim et al. [12] established necessary and sufficient optimality conditions and duality results for weakly efficient solutions of nondifferentiable multiobjective fractional programming problems.

In this study we have established necessary and sufficient optimality conditions under generalized convexity using the tool-right upper-Dini-derivative for a general minimax programming problem.

In [10], Gaydu, Geoffroy and Marcelin established necessary condition and sufficient conditions for the weak minimizers and the strong minimizers of the optimization problem (SP).

Alicherry et al.[9] established necessary and sufficient conditions for interference-free link schedule and proposed a simple greedy algorithm based on the UDG model.

An American pre-emptive strike would also re-establish necessary red lines for North Korea and other countries in similar circumstances.

"Stability in the banking sector is best achieved by establishing necessary capital buffers, having effective recovery and resolution arrangements, and appropriate supervision.

It must create a pathway to clean jobs and clean energy for all and establish necessary conditions for a sustainable and prosperous future for people, flora and fauna.

Mr. Barr opened a subcommittee hearing by asking Mr. Everson what steps would be taken "to ensure the privacy of personally identifiable information as the new agency establishes necessary databases that coordinate with other agencies of the government".

These findings can help the government establish necessary policies.