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1.
为了进一步研究模糊值函数的性质,基于模糊值函数结构元解析表述的有关理论,首先以广义模糊数序关系为前提,通过模糊不等式限定运算,研究了模糊值函数的凸性,并给出了凸模糊值函数的判定方法与性质.进一步通过结构序的排序方法,将模糊值函数的有关研究转换为对其伴随函数的研究,给出了模糊值函数伴随单调性,伴随凸性的定义,并研究了伴随凸模糊值函数的性质,以及伴随单调性和伴随凸性的判定方法.最后对单调性与伴随单调性,以及凸性与伴随凸性的关系进行了分析.  相似文献   

2.
二层广义凸规划及其性质   总被引:4,自引:0,他引:4  
讨论了二层规划的性质 ,在一些凸性和广义凸性假设下 ,讨论了下层极值函数和上层目标函数的凸性、拟凸性和连续性性质 ,获得了五个定理 ,并予以证明 .  相似文献   

3.
定义了一完全对称函数并研究该称函数的Schur凸性,Schur乘性凸性及Schur调和凸性,作为应用探讨了与其相关的一些不等式.  相似文献   

4.
陈秀宏 《应用数学》2004,17(3):370-374
本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 .  相似文献   

5.
一致不变凸多目标规划的有效性条件和对偶性   总被引:1,自引:0,他引:1  
作者对多目标规划引进一致不变凸的概念,用来综合规划所涉及函数的不变凸性,而不是用单个函数的不变凸性.考虑了涉及这样函数的多目标规划解的有效性和Mond-Weir对偶性.  相似文献   

6.
本文讨论不可微函数的强伪不变凸性和不变伪单调性之间的关系,还讨论了不可微函数的伪不变凸性与半严格预拟不变凸性.此外,还给出了一个集值映射的不变伪单调的等价定义.  相似文献   

7.
给出赋Luxemburg范数的Orlicz函数空间的紧一致凸、弱紧一致凸、紧局部一致凸、弱紧局部一致凸和k-drop凸的判据,并且据此得到在Orlicz函数空间中这些凸性的等价关系.  相似文献   

8.
在Goetschel-Voxman所定义的序关系下,首先讨论了模糊值函数的凸性,得到了凸模糊值函数的若干充分条件,并证明了凸模糊值函数的Jensen不等式;其次,讨论了凸模糊值函数的次可微性,给出了次微分的若干重要性质,并得到了次可微条件下取得最优解的充分必要条件以及若干个次可微的充分条件.  相似文献   

9.
研究十二类广义凸函数相关集合的对称性问题及其对应函数的中点凸性问题.证明了其中的十个集合具有对称性,应用反例说明了余下的两个集合不必具有对称性.证明了六个集合对应的函数具有中点凸性,应用反例说明了余下六个集合对应的函数不必具有中点凸性.  相似文献   

10.
解决了一类与积分有关的函数的凸性问题,其中的定理都是一些已知结果的加强.作为应用,它给出了二类平均和一个与Gamma函数有关的函数的凸性.  相似文献   

11.
The problem of continuously dynamic multiobjective optimization, or multiobjective control, is discussed. The concepts of nondominated controls and viable controls are introduced. For a class of nonlinear dynamic systems, the convexity of their controlled Carathéodory trajectories is proved. Based on this convexity, sufficient conditions are given for the solution of a multiobjective control problem to be obtained in terms of solutions of weighting problems.This work was partly done at the Huazhong University of Science and Technology, Wuhan, China. The author is indebted to Professor Chen Ting for his advice. The author wishes to thank Professor G. Leitmann for his favorable comments. The author is also grateful to Ms. Mary S. Linn at the University of Kansas, who helped him improve the English presentation of this paper.  相似文献   

12.
作者介绍了一种基于向量值延拓函数的广义增广拉格朗日函数,建立了基于广义增广拉格朗日函数的集值广义增广拉格朗日对偶映射和相应的对偶问题,得到了相应的强对偶和弱对偶结果,将所获结果应用到约束向量优化问题.该文的结果推广了一些已有的结论.  相似文献   

13.
NP-hardness is established for the problem whose instance is a system of linear inequalities defining a polytopeP, and whose question is whether, onP, the global maximum of the Euclidean norm is attained at more than one vertex ofP. The NP-hardness persists even for the restricted problem in whichP is a full-dimensional parallelotope with one vertex at the origin. This makes it possible to establish NP-hardness for other uniqueness problems, including some from pseudoboolean programming and computational convexity.Research of the first author was supported in part by the Deutsche Forschungsgemeinschaft. Research of the second author was supported in part by the National Science Foundation.  相似文献   

14.
Pooja Gupta 《Optimization》2018,67(8):1157-1167
In this paper, we consider a nonsmooth vector optimization problem involving locally Lipschitz generalized approximate convex functions and find some relations between approximate convexity and generalized approximate convexity. We establish relationships between vector variational inequalities and nonsmooth vector optimization problem using the generalized approximate convexity as a tool.  相似文献   

15.
Smoothing conditions in terms of Bézier coefficients of piecewise rational functions on an arbitrary triangulation are derived. This facilitates the solution of the problem of bivariate rational spline interpolation, with or without convexity constraints, particularly on the three and four-directional meshes. For such a triangulation, we also derive the conformality condition that a bivariate rationale spline function must satisfy, and we demonstrate the interpolation scheme with a low-degree example.The research of this author was supported by NSF Grant # DMS-92-06928.  相似文献   

16.
The optimization problem of a nonlinear real function over the weakly-efficient set associated to a nonlinear multi-objective program is examined. Necessary first-order conditions for a suboptimal solution are proposed, assuming the convexity of the multi-objective program. Estimations of the optimal value are established and an algorithm for finding suboptimal solutions is proposed. The optimal value is approximated to any prescribed degree of accuracy using a weakly-efficient suboptimal solution.This work was done while the author was preparing his Ph.D. Thesis at the University of Melbourne, Australia. The author is thankful to Dr. B. D. Craven for his suggestions and helpful discussions and to Professor W. Stadler and the anonymous referees for their helpful comments and corrections.  相似文献   

17.
In the present paper, we discuss the isoperimetric problems for domains with partly known boundaries, i.e., the problem of determining a domain that minimizes the capacity functional in the class of plain double-connected domains having the same fixed area and outer boundary. The formulas for capacity variations obtained in this paper allows us to formulate necessary conditions.It is proved that the convexity of the fixed outer boundary implies the convexity of the inner boundary corresponding to an optimal domain. Then, we discuss the case where the fixed part of the boundary is a square.Further, we consider similar problems with more complicated functionals. We introduce the concept of a minimal function in the class of equimeasurable functions. This concept allows us to unify the approach to all of these problems. At the end, we produce a hypothesis that, if proved, would enable us to characterize the shape of the optimal domains in the isoperimetric problems mentioned above.The author wishes to express his appreciation to Dr. K. A. Lurie for his help and unceasing attention.  相似文献   

18.
Under differentiability assumptions, Fritz John Sufficient optimality conditions are proved for a nonlinear programming problem in which the objective function is assumed to be quasiconvex and the constraint functions are assumed to quasiconcave/strictly pseudoconcave. Duality theorems are proved for Mond-Weir type duality under the above generalized convexity assumptions.The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant No. A-5319. The authors are thankful to Professor B. Mond for suggestions that improved the original draft of the paper.  相似文献   

19.
A vector variational inequality is studied. The paper deals with existence theorems for solutions under convexity assumptions and without convexity assumptions.This research was partially supported by the Italian Research Council (CNR), Group for Functional Analysis and Applications (GNAFA), and was carried out while the author was Visiting Professor at the Department of Mathematics, University of Pisa, September–November, 1989.  相似文献   

20.
We derive a weak Maximum Principle for nonsmooth optimal control problem involving mixed constraints under some convexity assumptions. Notably we consider problems with possibly nonsmooth mixed constraints. A nonsmooth version of the positive linear independence of the gradients with respect to the control of the mixed constraints plays a key role in validation of our main result. The first author was support by FEDER and FCT-Portugal, grants POSC/EEA/SRI/61831/2004 and SFRH/BSAB/781/2008. G.N. Silva thanks the financial support of CNPq grant 200875/06-0 and FAPESP grant 07-5226-6.  相似文献   

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