共查询到19条相似文献,搜索用时 46 毫秒
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该文研究一类目标和约束函数均带有不确定信息的凸优化问题的鲁棒近似解.首先,在闭凸锥约束品性假设下,得到了该不确定优化问题关于近似解的最优性条件.然后,引入所研究不确定优化问题的近似鞍点的概念,并给出了近似解的鞍点刻划. 相似文献
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该文研究了一类带不确定参数的多目标分式半无限优化问题.首先借助鲁棒优化方法,引入该不确定多目标分式优化问题的鲁棒对应优化模型,并借助Dinkelbach方法,将该鲁棒对应优化模型转化为一般的多目标优化问题.随后借助一种标量化方法,建立了该优化问题的标量化问题,并刻画了它们的解之间的关系.最后借助一类鲁棒型次微分约束规格,建立了该不确定多目标分式优化问题拟近似有效解的鲁棒最优性条件. 相似文献
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本文利用极值原理在Fréchet次微分下研究了非光滑多目标优化问题的最优性条件.首先,研究了非光滑半无限多目标优化问题的必要性条件.随后,建立了非光滑多目标优化问题Henig真有效解的必要条件. 相似文献
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本文讨论定义于Banach空间的多目标数学规划,得到一些ε-最优解和(弱)有效解的必要条件,充分条件和必要充分条件。 相似文献
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在广义凸性假设下,给出了集合proximal真有效点的线性标量化,并在此基础上证明了它与Benson真有效点和Borwein真有效点的等价性.将这些结果应用到多目标优化问题上,得到proximal真有效解的最优性条件.最后,利用proximal次微分,得到了proximal真有效解的模糊型最优性条件. 相似文献
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AbstractWe present optimality conditions for a class of nonsmooth and nonconvex constrained optimization problems. To achieve this aim, various well-known constraint qualifications are extended based on the concept of tangential subdifferential and the relations between them are investigated. Moreover, local and global necessary and sufficient optimality conditions are derived in the absence of convexity of the feasible set. In addition to the theoretical results, several examples are provided to illustrate the advantage of our outcomes. 相似文献
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Journal of Optimization Theory and Applications - This paper is devoted to presenting new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly... 相似文献
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Global Optimality Conditions for Nonconvex Optimization 总被引:4,自引:0,他引:4
Alexander S. Strekalovsky 《Journal of Global Optimization》1998,12(4):415-434
In this paper we give an analytical equivalent for the inclusion of a set to the Lebesque set of a convex function. Using this results, we obtain global optimality conditions (GOC) related to classical optimization theory for convex maximization and reverse-convex optimization. Several examples illustrate the effectiveness of these optimality conditions allowing to escape from stationary points and local extremums. 相似文献
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Hong-Zhi Wei Chun-Rong Chen Sheng-Jie Li 《Journal of Optimization Theory and Applications》2018,177(3):835-856
In this paper, by virtue of the image space analysis, the general scalar robust optimization problems under the strictly robust counterpart are considered, among which, the uncertainties are included in the objective as well as the constraints. Besides, on the strength of a corrected image in a new type, an equivalent relation between the uncertain optimization problem and its image problem is also established, which provides an idea to tackle with minimax problems. Furthermore, theorems of the robust weak alternative as well as sufficient characterizations of robust optimality conditions are achieved on the frame of the linear and nonlinear (regular) weak separation functions. Moreover, several necessary and sufficient optimality conditions, especially saddle point sufficient optimality conditions for scalar robust optimization problems, are obtained. Finally, a simple example for finding a shortest path is included to show the effectiveness of the results derived in this paper. 相似文献
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Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems 总被引:1,自引:0,他引:1
In this paper, we introduce a new concept of ϵ-efficiency for vector optimization problems. This extends and unifies various notions of approximate solutions in the literature.
Some properties for this new class of approximate solutions are established, and several existence results, as well as nonlinear
scalarizations, are obtained by means of the Ekeland’s variational principle. Moreover, under the assumption of generalized
subconvex functions, we derive the linear scalarization and the Lagrange multiplier rule for approximate solutions based on
the scalarization in Asplund spaces. 相似文献
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In this paper, some necessary and sufficient optimality conditions for the weakly efficient solutions of vector optimization
problems (VOP) with finite equality and inequality constraints are shown by using two kinds of constraints qualifications
in terms of the MP subdifferential due to Ye. A partial calmness and a penalized problem for the (VOP) are introduced and
then the equivalence between the weakly efficient solution of the (VOP) and the local minimum solution of its penalized problem
is proved under the assumption of partial calmness.
This work was supported by the National Natural Science Foundation of China (10671135), the Specialized Research Fund for
the Doctoral Program of Higher Education (20060610005) and the National Natural Science Foundation of Sichuan Province (07ZA123).
The authors thank Professor P.M. Pardalos and the referees for comments and suggestions. 相似文献
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The concept of ɛ-approximate optimal solution as widely used in nonconvex global optimization is not quite adequate, because
such a point may correspond to an objective function value far from the true optimal value, while being infeasible. We introduce
a concept of essential ɛ-optimal solution, which gives a more appropriate approximate optimal solution, while being stable
under small perturbations of the constraints. A general method for finding an essential ɛ-optimal solution in finitely many
steps is proposed which can be applied to d.c. programming and monotonic optimization. 相似文献
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X. Q. Yang 《Journal of Global Optimization》2004,30(2-3):271-284
Second-order optimality conditions are studied for the constrained optimization problem where the objective function and the constraints are compositions of convex functions and twice strictly differentiable functions. A second-order sufficient condition of a global minimizer is obtained by introducing a generalized representation condition. Second-order minimizer characterizations for a convex program and a linear fractional program are derived using the generalized representation condition 相似文献
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X. Q. Yang 《Journal of Global Optimization》2004,30(2):271-284
Second-order optimality conditions are studied for the constrained optimization problem where the objective function and the constraints are compositions of convex functions and twice strictly differentiable functions. A second-order sufficient condition of a global minimizer is obtained by introducing a generalized representation condition. Second-order minimizer characterizations for a convex program and a linear fractional program are derived using the generalized representation condition 相似文献