共查询到20条相似文献,搜索用时 31 毫秒
1.
引入了集值集值C-τ-半预不变凸概念,证明了集值集值C-τ-半预不变凸优化问题的局部弱有效元是弱有效元,给出了集值预不变凸变分不等式作为集值C-τ-半预不变凸优化问题的充分条件和必要条件,这些结果推广了文[1-4]的相应结果。 相似文献
2.
讨论拓扑向量空间中无约束集值优化问题的最优性条件问题.利用集值映射的Dini方向导数,在广义锥-预不变凸性条件下,建立了集值优化问题关于弱极小元和强极小元的最优性充分必要条件. 相似文献
3.
Weak minimizers,minimizers and variational inequalities for set-valued functions. A blooming wreath?
Giovanni P. Crespi 《Optimization》2017,66(12):1973-1989
Recently, necessary and sufficient conditions in terms of variational inequalities have been introduced to characterize minimizers of convex set-valued functions. Similar results have been proved for a weaker concept of minimizers and weaker variational inequalities. The implications are proved using scalarization techniques that eventually provide original problems, not fully equivalent to the set-valued counterparts. Therefore, we try, in the course of this note, to close the network among the various notions proposed. More specifically, we prove that a minimizer is always a weak minimizer, and a solution to the stronger variational inequality always also a solution to the weak variational inequality of the same type. As a special case, we obtain a complete characterization of efficiency and weak efficiency in vector optimization by set-valued variational inequalities and their scalarizations. Indeed, this might eventually prove the usefulness of the set optimization approach to renew the study of vector optimization. 相似文献
4.
Truong Xuan Duc Ha 《Journal of Mathematical Analysis and Applications》2010,364(1):156-170
In this paper we consider, for the first time, approximate Henig proper minimizers and approximate super minimizers of a set-valued map F with values in a partially ordered vector space and formulate two versions of the Ekeland variational principle for these points involving coderivatives in the sense of Ioffe, Clarke and Mordukhovich. As applications we obtain sufficient conditions for F to have a Henig proper minimizer or a super minimizer under the Palais-Smale type conditions. The techniques are essentially based on the characterizations of Henig proper efficient points and super efficient points by mean of the Henig dilating cones and the Hiriart-Urruty signed distance function. 相似文献
5.
By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational
principle for a set-valued map. J. Optim. Theory Appl., 124, 187–206 (2005)] established a new version of Ekeland’s variational principle for set-valued maps, which is expressed by
the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement
of Ha’s version of set-valued Ekeland’s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev
theorem. From the improved Ha’s version, we deduce a Caristi-Kirk’s fixed point theorem and a Takahashi’s nonconvex minimization
theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other. 相似文献
6.
7.
An Inverse Problem of Identifying the Radiative Coefficient in a Degenerate Parabolic Equation 总被引:5,自引:0,他引:5
The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle coefficients are assumed to be strictly positive definite, the mathematical model discussed in this paper belongs to the second order parabolic equations with non-negative characteristic form, namely, there exists a degeneracy on the lateral boundaries of the domain. Based on the optimal control framework, the problem is transformed into an optimization problem and the existence of the minimizer is established. After the necessary conditions which must be satisfied by the minimizer are deduced, the uniqueness and stability of the minimizer are proved. By minor modification of the cost functional and some a priori regularity conditions imposed on the forward operator, the convergence of the minimizer for the noisy input data is obtained in this paper. The results can be extended to more general degenerate parabolic equations. 相似文献
8.
Theorems of the Alternative and Optimization with Set-Valued Maps 总被引:16,自引:0,他引:16
X. M. Yang X. Q. Yang G. Y. Chen 《Journal of Optimization Theory and Applications》2000,107(3):627-640
In this paper, the concept of generalized cone subconvexlike set-valued mapsis presented and a theorem of alternative for the system of generalizedinequality–equality set-valued maps is established. By applying thetheorem of the alternative and other results, necessary and sufficientoptimality conditions for vector optimization problems with generalizedcone subconvexlike set-valued maps are obtained. 相似文献
9.
该文研究局部凸空间中受集值约束的集值优化问题的超有效解. 证明了ic -锥-类凸集值映射的一个有用性质, 并以此性质为主要工具, 得到了ic -锥-类凸集值向量优化问题超有效解的最优性条件和鞍点定理. 相似文献
10.
This paper deals with set-valued equilibrium problems under conditions of pseudo-monotonicity. Concepts such as strict quasi-convexity, hemicontinuity and pseudo-monotonicity for extended real set-valued mappings are introduced and applied to obtain results on the existence of solutions of set-valued equilibrium problems generalizing those in the literature in the pseudo-monotone case. Applications to Browder variational inclusions under weakened conditions are given. In particular, it is shown that the upper semicontinuity from line segments of the involved pseudo-monotone set-valued operator is not needed in the whole space when solving Browder variational inclusions. 相似文献
11.
In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature. 相似文献
12.
This paper deals with higher-order optimality conditions of set-valued optimization problems. By virtue of the higher-order derivatives introduced in (Aubin and Frankowska, Set-Valued Analysis, Birkhäuser, Boston, [1990]) higher-order necessary and sufficient optimality conditions are obtained for a set-valued optimization problem whose constraint condition is determined by a fixed set. Higher-order Fritz John type necessary and sufficient optimality conditions are also obtained for a set-valued optimization problem whose constraint condition is determined by a set-valued map. 相似文献
13.
该文讨论局部凸空间中的约束集值优化问题. 首先, 在生成锥内部凸-锥-类凸假设下, 建立了Henig真有效解在标量化和Lagrange乘子意义下的最优性条件. 其次, 对集值Lagrange映射引入Henig真鞍点的概念, 并用这一概念刻画了Henig真有效解. 最后, 引入了一个标量Lagrange对偶模型, 并得到了关于Henig真有效解的对偶定理. 另外, 该文所得结果均不需要约束序锥有非空的内部. 相似文献
14.
本文首先建立了实值非负函数关于集值序增函数的集值Riemann-Stieltjes积分,并讨论了集值Riemann-Stieltjes积分的性质,给出了集值Riemann-Stieltjes可积的充要条件,最后引入了集值Riemann-Stieltjes随机积分. 相似文献
15.
Nguyen Le Hoang Anh 《Positivity》2016,20(2):499-514
In this paper, we introduce a notion of higher-order Studniarski epiderivative of a set-valued map and study its properties. Then, we discuss their applications to optimality conditions in set-valued optimization. Higher-order optimality conditions for strict and weak efficient solutions of a constrained set-valued optimization problem are established. Some remarks on the existing results in the literature are given from our results. 相似文献
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17.
In this paper, generalized mth-order contingent epiderivative and generalized mth-order epiderivative of set-valued maps are introduced, respectively. By virtue of the generalized mth-order epiderivatives, generalized necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a fixed set. Generalized Kuhn–Tucker type necessary and sufficient optimality conditions are also obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a set-valued map. 相似文献
18.
V. Jeyakumar S. Srisatkunarajah 《Journal of Optimization Theory and Applications》2009,140(2):239-247
We present new conditions for a Karush-Kuhn-Tucker point to be a global minimizer of a mathematical programming problem which
may have many local minimizers that are not global. The new conditions make use of underestimators of the Lagrangian at the
Karush-Kuhn-Tucker point. We establish that a Karush-Kuhn-Tucker point is a global minimizer if the Lagrangian admits an underestimator,
which is convex or, more generally, has the property that every stationary point is a global minimizer. In particular, we
obtain sufficient conditions by using the fact that the biconjugate function of the Lagrangian is a convex underestimator
at a point whenever it coincides with the Lagrangian at that point. We present also sufficient conditions for weak and strong
duality results in terms of underestimators.
The authors are grateful to Professor Gue Myung Lee, Pukyong National University, Korea, and the referees for their comments
and suggestions which have contributed to the final preparation of the paper. The work was partially supported by the Australian
Research Council Discovery Project Grant. 相似文献
19.
D. E. Ward 《Journal of Optimization Theory and Applications》1994,80(3):551-571
In nonlinear programming, sufficient conditions of orderm usually identify a special type of local minimizer, here termed a strict local minimizer of orderm. In this paper, it is demonstrated that, if a constraint qualification is satisfied, standard sufficient conditions often characterize this special sort of minimizer. The first- and second-order cases are treated in detail. Necessary conditions for weak sharp local minima of orderm, a larger class of local minima, are also presented.This paper was completed during a sabbatical leave at the University of Waterloo. The author is grateful for the help and support of the Department of Combinatorics and Optimization. The helpful comments of the referees are also appreciated. 相似文献
20.
In convex optimization the significance of constraint qualifications is evidenced by the simple duality theory, and the elegant subgradient optimality conditions which completely characterize a minimizer. However, the constraint qualifications do not always hold even for finite dimensional optimization problems and frequently fail for infinite dimensional problems. In the present work we take a broader view of the subgradient optimality conditions by allowing them to depend on a sequence of ε-subgradients at a minimizer and then by letting them to hold in the limit. Liberating the optimality conditions in this way permits us to obtain a complete characterization of optimality without a constraint qualification. As an easy consequence of these results we obtain optimality conditions for conic convex optimization problems without a constraint qualification. We derive these conditions by applying a powerful combination of conjugate analysis and ε-subdifferential calculus. Numerical examples are discussed to illustrate the significance of the sequential conditions. 相似文献