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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
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关于凸逼近,共凸逼近的各种逼近阶的估计在近十多年来已引起了相当的重视和较多的研究,因为保形渐近的思想在实际问题中有着十分重要的意义。相比较而言,共凸逼近的的研究比凸逼近的情况要复杂,因此,不少关于凸逼近已得到解决的问题对于共凸逼近仍没有结果,关于共凸逼近,1984,Atacir,Sermin证明了。 相似文献
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无限维空间拟凸映射多目标最优化问题解集的连通性 总被引:10,自引:1,他引:10
本文在一个无限格中引入了拟凸、强拟凸和严格拟凸映射。并在约束集为紧凸条件下,证明了相应的多目标规划问题之有效解集和弱有效解集连通性结果。 相似文献
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在拓扑向量空间中,利用Ky Fan截口定理得到一个锥凸向量拟均衡问题弱Pareto解的存在性结果.作为该结果的应用,得到了一个对称向量拟均衡问题在支付映射为锥凸条件下弱Pareto解的存在性定理.该定理在较弱的条件下回答了Fu在文献[1]中提出的第二个问题,即在支付映射为锥凸且连续的条件下对称向量拟均衡问题的弱Pareto解是否存在.最后在赋范线性空间中研究了锥凸对称向量拟均衡问题弱Pareto解集的通有稳定性. 相似文献
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给出了求解一类无界非凸区域上不动点问题的路径跟踪方法.在适当的条件下,给出了不动点存在性的构造性证明,从而得到了路径跟踪方法的全局收敛性结果.研究结果为计算无界非凸区域上不动点问题提供了一种全局收敛性方法. 相似文献
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本文研究了Rn中凸集上不变的赋值函数与凸体的投影问题.利用赋值函数的方法,我们获得了凸体在任意维平面上投影的Cauchy公式和Kubota公式,这些结果推广了经典的Cauchy公式和Kubota公式. 相似文献
11.
Fabio Tardella 《Optimization Letters》2008,2(3):363-375
Convex envelopes are a very useful tool in global optimization. However finding the exact convex envelope of a function is
a difficult task in general. This task becomes considerably simpler in the case where the domain is a polyhedron and the convex
envelope is vertex polyhedral, i.e., has a polyhedral epigraph whose vertices correspond to the vertices of the domain. A further simplification is possible
when the convex envelope is sum decomposable, i.e., the convex envelope of a sum of functions coincides with the sum of the convex envelopes of the summands. In this
paper we provide characterizations and sufficient conditions for the existence of a vertex polyhedral convex envelope. Our
results extend and unify several results previously obtained for special cases of this problem. We then characterize sum decomposability
of vertex polyhedral convex envelopes, and we show, among else, that the vertex polyhedral convex envelope of a sum of functions
coincides with the sum of the vertex polyhedral convex envelopes of the summands if and only if the latter sum is vertex polyhedral. 相似文献
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A class of nonconvex minimization problems can be classified as hidden convex minimization problems. A nonconvex minimization problem is called a hidden convex minimization problem if there exists an equivalent transformation such that the equivalent transformation of it is a convex minimization problem. Sufficient conditions that are independent of transformations are derived in this paper for identifying such a class of seemingly nonconvex minimization problems that are equivalent to convex minimization problems. Thus, a global optimality can be achieved for this class of hidden convex optimization problems by using local search methods. The results presented in this paper extend the reach of convex minimization by identifying its equivalent with a nonconvex representation. 相似文献
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A.R. Nazemi 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1696-1705
This paper proposes a feedback neural network model for solving convex nonlinear programming (CNLP) problems. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using some examples. 相似文献
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In this paper, several Lagrange multiplier characterizations of the solution set of a convex infinite programming problem
are given. Characterizations of solution sets of cone-constrained convex programs are derived as well. The procedure is then
adopted to a semi-convex problem with convex constraints. For this problem, we present firstly a necessary and sufficient
condition for optimality and secondly a characterization of its optimal solution set, based on a Lagrange multiplier associated
with a given solution and on directional derivatives of the objective function.
相似文献
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Kazimierz Malanowski 《Mathematical Programming》1985,33(3):352-361
We consider a family of convex programming problems that depend on a vector parameter, characterizing those values of parameters at which solutions and associated Lagrange multipliers are Gâteaux differentiable.These results are specialized to the problem of the metric projection onto a convex set. At those points where the projection mapping is not differentiable the form of Clarke's generalized derivative of this mapping is derived. 相似文献
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Xiuguo Lian 《Journal of Mathematical Analysis and Applications》2007,327(1):79-87
In this paper we provide a ball separation property of bounded convex sets in a Hilbert space. As a consequence, we obtain a representation form of convex closures and two results about convex functionals. 相似文献
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L. Z. Liao 《Journal of Optimization Theory and Applications》2005,124(1):207-226
In this paper, we present a continuous method for convex programming (CP) problems. Our approach converts first the convex problem into a monotone variational inequality (VI) problem. Then, a continuous method, which includes both a merit function and an ordinary differential equation (ODE), is introduced for the resulting variational inequality problem. The convergence of the ODE solution is proved for any starting point. There is no Lipschitz condition required in our proof. We show also that this limit point is an optimal solution for the original convex problem. Promising numerical results are presented.This research was supported in part by Grants FRG/01-02/I-39 and FRG/01-02/II-06 of Hong Kong Baptist University and Grant HKBU2059/02P from the Research Grant Council of Hong Kong.The author thanks Professor Bingsheng He for many helpful suggestions and discussions. The author is also grateful for the comments and suggestions of two anonymous referees. In particular, the author is indebted to one referee who drew his attention to References 15, 17, 18. 相似文献
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Global optimization problems involving the minimization of a product of convex functions on a convex set are addressed in
this paper. Elements of convex analysis are used to obtain a suitable representation of the convex multiplicative problem
in the outcome space, where its global solution is reduced to the solution of a sequence of quasiconcave minimizations on
polytopes. Computational experiments illustrate the performance of the global optimization algorithm proposed.
相似文献
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《Optimization》2012,61(3-4):301-314
In [9] it is shown that the one-sided derivatives of parametric linear semi-infinite programs can be expressed in terms of one-sided cluster points of solutions and Lagrange-multipliers of the perturbed problem. In this paper convex programs on Banach-spaces are studied. We generalize the results in [9] to this case. The analysis is based on convex duality theory [2]. 相似文献