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函数强伪凸性与映射强伪单调性 总被引:1,自引:0,他引:1
杨益民 《高等学校计算数学学报》2000,22(2):141-146
1 引 言Schaible在[1]中引入七类单调映射,并证明对其中六类,函数的某种广义凸性都和相应的梯度单调性等价,只有函数强伪凸和梯度强伪单调的等价性是否成立作为公开问题.其后,Schaible又在[2]中通过一个例子否定了两者的等价性,并引入了较弱的函数强伪凸和映射强伪单调的概念,在函数二次可微的条件下证明了函数强伪凸和梯度强伪单调等价.我们将引入强于[2]中概念的强伪凸和强伪单调性,对给出的定义,不附加条件便可保证函数强伪凸性和梯度强伪单调性等价.同时,对[2]中的一个错误予以指出,并给出正确的反例.还就[1]中问题给出远比[2]中简… 相似文献
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研究在锥伪单调、锥拟凸、锥严格拟凸和次连续条件下几类二元向量平衡问题解的关系,利用KyFan不动点定理证明了解的存在性。 相似文献
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本文用Ekeland,L变分原理及分析中的几何方法研究了抽象的广义方向导数和广义梯度中的切锥包含问题,给出了一个切锥包含定理. 相似文献
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广义伪凸函数的一个性质杨新民(重庆师范学院数学系,630047)关键词广义伪凸,严格广义伪凸,判别准则.分类号AMS(1991)90C25,26B25/CCLO221.2设B是R ̄n中单位开球,f:R ̄n→R在点x处称为Lipschitz函数,即存在... 相似文献
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拓扑向量空间中非光滑向量极值问题的最优性条件与对偶 总被引:1,自引:0,他引:1
本文提出了向量值函数的锥D-s凸,锥D-s拟凸,s右导数及锥D-s伪凸等新概念,探讨了锥D-s凸函数的有关性质,建立了带约束非光滑向量极值问题(VP)的最优性必要条件与涉及锥D-s凸(拟凸,伪凸)函数的约束极值问题(VP)的最优性充分条件,给出了原问题(VP)与其Mond-Weir型对偶问题的弱对偶与强对偶结论,揭示了(VP)的局部锥D-(弱)有效解与整体锥D-(弱)有效解,(VP)的锥D-弱有效解与锥D-有效解的关系,所得结果拓广了凸规划及部分广义凸规划的有关结论. 相似文献
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《Optimization》2012,61(3):327-338
In this article, two types of cone-pseudomonotone bifunctions have been introduced and the weaker form of pseudomonotonicity is used to establish an existence theorem for a Stampacchia-kind vector variational inequality problem given in terms of bifunctions. For a vector optimization problem, the necessary and sufficient optimality conditions in terms of an associated vector variational inequality problem have been established using a generalized form of cone pseudoconvexity of objective function. 相似文献
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《Optimization》2012,61(4):627-643
Recently, the so-called second order cone optimization problem has received much attention, because the problem has many applications and the problem can in theory be solved efficiently by interior-point methods. In this note we treat duality for second order cone optimization problems and in particular whether a nonzero duality gap can be obtained when casting a convex quadratically constrained optimization problem as a second order cone optimization problem. Furthermore, we also discuss the p -order cone optimization problem which is a natural generalization of the second order case. Specifically, we suggest a new self-concordant barrier for the p -order cone optimization problem. 相似文献
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拓扑向量空间中锥半连续性与锥拟凸映射 总被引:2,自引:0,他引:2
对于拓扑向量空间中的几个锥拟凸映射,讨论了它们之间的若干关系,同时,对锥半连续及锥上半连续映射的锥拟凸性给出了一些结果。 相似文献
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对于有限维Euclid空间中带两个参数的ak-较多锥,本文讨论了它与正锥以及有关较多锥类之间的若干关系.同时,还得到此类锥的一些基本性质. 相似文献
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Ashkan Fakhri 《Optimization》2016,65(5):1023-1038
This paper tries to minimize the sum of a linear and a linear fractional function over a closed convex set defined by some linear and conic quadratic constraints. At first, we represent some necessary and sufficient conditions for the pseudoconvexity of the problem. For each of the conditions, under some reasonable assumptions, an appropriate second-order cone programming (SOCP) reformulation of the problem is stated and a new applicable solution procedure is proposed. Efficiency of the proposed reformulations is demonstrated by numerical experiments. Secondly, we limit our attention to binary variables and derive a sufficient condition for SOCP representability. Using the experimental results on random instances, we show that the proposed conic reformulation is more efficient in comparison with the well-known linearization technique and it produces more eligible cuts for the branch and bound algorithm. 相似文献
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Thabet Abdeljawad 《Numerical Functional Analysis & Optimization》2013,34(5):477-495
In this article, a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute value property. In particular, if E is a Dedekind complete Banach lattice, then, together with its absolute value norm, satisfy the desired properties. 相似文献
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Lagrangian Duality and Cone Convexlike Functions 总被引:1,自引:0,他引:1
In this paper, we consider first the most important classes of cone convexlike vector-valued functions and give a dual characterization
for some of these classes. It turns out that these characterizations are strongly related to the closely convexlike and Ky
Fan convex bifunctions occurring within minimax problems. Applying the Lagrangian perturbation approach, we show that some
of these classes of cone convexlike vector-valued functions show up naturally in verifying strong Lagrangian duality for finite-dimensional
optimization problems. This is achieved by extending classical convexity results for biconjugate functions to the class of
so-called almost convex functions. In particular, for a general class of finite-dimensional optimization problems, strong
Lagrangian duality holds if some vector-valued function related to this optimization problem is closely K-convexlike and satisfies some additional regularity assumptions. For K a full-dimensional convex cone, it turns out that the conditions for strong Lagrangian duality simplify. Finally, we compare
the results obtained by the Lagrangian perturbation approach worked out in this paper with the results achieved by the so-called
image space approach initiated by Giannessi. 相似文献
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非线性二阶常微分方程的正周期解 总被引:2,自引:0,他引:2
讨论一类非线性二阶常微分方程的周期解问题 ,利用Banach空间锥上的不动点定理得到了正周期解的存在性和多重性结果 ,大大改进了文献 [1 ]的结果 相似文献
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该文通过构造一个特殊的锥,利用锥压缩与锥拉伸不动点定理,研究了一类二阶奇异微分方程边值问题两个正解的存在性,改进了最近的一些结果. 相似文献