在广义凸性条件下，建立了弱对偶性定理。
Weak duality theorem is established under generalized convexity conditions.
接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
最后，利用择一性定理，获得了含不等式和等式约束的广义次似凸集值映射向量最优化问题的最优性条件。
Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.
用集合的近似凸性研究函数的拟凸性。在较弱假设下，获得了拟凸性的一些等价条件。
Quasiconvex functions are studied by applying nearly convexity of sets. Under weaker assumptions, some equivalent conditions for quasiconvexity are derived.
用集合的近似凸性研究函数的预不变凸性，在较弱的假设下获得了预不变凸性的一些等价条件。
Preconvex functions are studied by applying nearly convexity of sets in this paper. Under weaker assumptions, some equivalent conditions for preconvexity are derived.
并且通过把该交叉规划转化为特殊的凸二次双水平规划，给出这类交叉规划的最优性条件和求解算法。
Furthermore, it gives an optimum condition and a simple algorithm of the special interaction programming by changing it into a special convex quadratic bilevel programming.
并在广义凸性和广义单调性的条件下，给出了隐向量均衡问题的解的存在性。
In addition, under the generalized convexity and generalized monotonicity, solution existence for implicit vector equilibrium problems is investigated.
在部分生成锥内部凸-锥-凸映射下，得到了既有等式约束又有不等式约束的向量优化问题弱有效解的最优性必要条件。
Under the conditions of Partial ic-convex like Maps, optimality necessary conditions of weak efficient solutions for vector optimization problems with equality and inequality constraints are obtained.
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。
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.
研究了线性约束的非线性凸规划问题，基于最优性的充要条件，提出了求解它的一个神经网络。
The paper studies the nonlinear programming problem with linear constraints. Based on its optimality conditions, a neural network for solving it is proposed.
在序线性空间中，利用次似凸映射的择一性定理，得出具有一般约束的向量极值问题的最优性条件。
Using the alternative theorem, the optimality conditions of vector extremum problems with generalized constraint are established in ordered linear space.
在一类适定性条件下，应用对数凸性方法证明了抛物方程终值问题具有平均稳定性。
Applying Logrithmic convex method, an average stability for the inverse parabolic problem with final observation is constructed under suitable correctness condition.
通过VB编程，完成非圆齿轮节曲线设计、根切校验、封闭性条件、凸性校验等计算，并输出设计结果，实现非圆齿轮节曲线的计算机辅助设计。
Through VB programming, complete the calculation of noncircular pitch design etc and export the design results, then achieve Computer Aided Design of noncircular gear pitch.
但本文表明，凸性规则既不是可投射性的充分条件也不是它的必要条件，因而概念空间方案并未解决新归纳之谜。
But I will show that the convexity rule is neither a sufficient condition nor a necessary condition. So the conceptual space solution can't solve the new riddle of induction.
利用差商代替难以计算的精确导数，结合既约梯度法的思想建立新的算法；在目标函数一致凸的条件下证明了既约差商法的整体收敛性。
The difference coefficient was used to replace the exact derivative which is difficult to be computed, and a new algorithm was presented by using the idea of reduced gradient method.
但本文表明，凸性规则既不是可投射性的充分条件也不是它的必要条件，因而概念空间方案并未解决新归纳之谜。
But I will show that the convexity rule is neither a sufficient condition nor a necessary condition. So the conceptual space solution ca...
利用凸性分析方法，在方程具有边界条件和正初始能量情况下得到整体解不存在的充分条件。
By making use of variational methods, we obtain two positive solutions ofp(x)-Laplace equation, which generlizes the corresponding relusts of Laplace equation.
利用凸性分析方法，在方程具有边界条件和正初始能量情况下得到整体解不存在的充分条件。
By making use of variational methods, we obtain two positive solutions ofp(x)-Laplace equation, which generlizes the corresponding relusts of Laplace equation.
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