necessary and sufficient optimality conditions 最优性充分必要条件并
optimality sufficient conditions 最优性充分条件
Then, we define a class of tangent cone F convexity in terms of the tangent cone directional derivative, and prove the sufficient optimality conditions for (VP).
然后利用正切锥方向导数定义一类正切锥F 凸函数类，并给出了（VP）正切锥真有效解的充分性条件；
Finally, optimality necessary and sufficient conditions for nonlinear convex semidefinite programming are proved.
并给出了非线性半定规划的最优性必要和充分条件。
It is proved that the optimality conditions are also sufficient if the objective function is a convex function of the plastic limit bending moment.
当目标函数是塑性极限弯矩凸函数时，证明了这一最优性条件也是最优解的充分条件。
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