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。
In 2 . 2 , we give a series of sufficient conditions for the existence and uniqueness of fixed point of increasing operator with u0 - convexity or q ( > 1 ) - homogeneity 在2 . 3中,作为前两节抽象结果的应用,我们讨论了具有凹凸性的hammerstein积分方程正解的存在唯一性问题。
Abstract : an approach to construct smooth and convexity preserving approximation of implicit surface is presented . it is piecewise cubic and its smoothness is higher than c1 文摘:给出了隐式曲面的光滑逼近和保凸逼近曲面的构造.所构造的曲面是分段三次的,其光滑度高于c1
A minimax theorem generally involves three assumption conditions : space structures on sets x and y , the continuity of the functions and the concavity and convexity of functions 一个极大极小定理一般涉及三个假设条件:集合x和y的空间结构,函数的连续性和函数的凹凸性。
The practical application indicates that the new design not only reduces the convexity of the roll profile obviously , but also leads to homogeneous attrition of rolls and low roll wear 生产实际应用表明,新设计的辊型不仅明显降低了板凸度,同时使轧辊磨损均匀,辊耗量大大下降。
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。
In the second chapter , the instruments ( for example , duration , convexity ect . ) and how to apply these instruments in market value analysis were formulated through examples 论文在第二章中介绍了市值分析中所用的工具(如持续期、凸度等) ,并通过实证分析阐述了这些工具的利用过程。
Finally , the convexity - concavity of the closed curve is detected . in the end , choi ' s pair - wise offset of polygon algorithm is improv ed based on the proposed curve intersection algorithm 文章最后完善了choi多边形等距偏移算法,并把本文提出的封闭曲线求交方法应用其中,用于自交点的确定。
Abstract : in this paper , a kind of more generalized arcwise convex functions : p - arcwise convexity functions is defined . on the basis of definitions , sufficient conditions of multiobjective programming are proved 文摘:定义了一类更一般的弧式凸函数,并在此基础上论证了其多目标规划的充分性条件。