We extend the determinant inequality of generalized real positive definite matrices that is advanced by paper [ 3 ] . moreover we give its convex inequality 摘要推广了文献[ 3 ]中的广义实正定矩阵的行列式不等式，同时给出了广义实正定矩阵的凸性不等式。
This paper discusses four sufficient optimality conditions for nonsmooth continuous - time nonliear multiobjective optimization problems under generalized convexity assumptions 在广义凸性假设下,讨论了非光滑连续时间非线性多目标优化问题的四个最优性充分条件。
Therefore , we solved the problem for p k + 1 under reasonable " convex assumption " . our results about the fully nonlinear elliptic equations may have its independent interest 对于与之相联系的完全非线性椭圆方程，我们得到的解的先验估计以及解的凸性的结论也是有意义的
As the directional derivative defined in this paper does n ' t show convexity , when its properties are considered , it is necessary to search for new ways to reach the conclusion 本文定义的广义方向导数在一般情况下不具有凸性，因而研究其性质时，要采用新的方法来得到类似的结论。
This property is independent with the convexity of the objective function and the line search used . therefore , the generated directions are descent directions of the objective function 这一个性质与目标函数的凸性以及线性搜索无关，因而，产生的搜索方向总是目标函数的下降方向。
Abstract : using the definitions of semi - locally star shaped set and generalized convexity for vector functions . we discuss the existence of efficient solutions for generalized multiobjective programming 文摘:本文利用1中的半局部星状集和向量函数的广义凸性，讨论了一类广义多目标规划有效解的存在性。
Martin ( ref . 36 ) proved the equivalence between some invexity and the case that every stationary point or kuhn - tucker point is a global minimum point for unconstrained or constrained scalar programming Martin在文献[ 36 ]中，证明了无约束或约束单目标规划中某类不变凸性与每个驻点(或k - t点)即为全局最优点的等价性。
In this axiom system , we made a study of the coherent measures of risk and convex measures of risk , which is extended from the coherent measures of risk , and proved its representation theorem 在一致性公理体系内，研究了一致风险测度的有关性质并由一致风险测度弱化部分条件后推广出凸性风险测度，并证明了它的表示定理。
A series of convex sufficient conditions of cubic natural splines is presented in case of equal intervals . under some hypotheses , several convex necessary conditions of cubic natural splines are obtained 摘要提出了在等距情形下三次自然样条函数一系列凸性的充分条件。在某些假定之下，还得到了一些三次自然样条函数凸性的必要条件。
This method combines the intrinsic solution algorithm and the convex combination morph algorithm , showing that the former has an excellent property of preserving the convexity of the intermediate triangulations " boundaries 该方法结合了内在解算法和凸组合变形算法，指出并证明了内在解算法具有保持中间网格边界的凸性这一优良特性。
