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101.
《Optimization》2012,61(6):699-716
We study a one-parameter regularization technique for convex optimization problems whose main feature is self-duality with respect to the Legendre–Fenchel conjugation. The self-dual technique, introduced by Goebel, can be defined for both convex and saddle functions. When applied to the latter, we show that if a saddle function has at least one saddle point, then the sequence of saddle points of the regularized saddle functions converges to the saddle point of minimal norm of the original one. For convex problems with inequality and state constraints, we apply the regularization directly on the objective and constraint functions, and show that, under suitable conditions, the associated Lagrangians of the regularized problem hypo/epi-converge to the original Lagrangian, and that the associated value functions also epi-converge to the original one. Finally, we find explicit conditions ensuring that the regularized sequence satisfies Slater's condition. 相似文献
102.
《Optimization》2012,61(8):1009-1028
Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization. 相似文献
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《Optimization》2012,61(2):323-338
Abstract New insights are presented from a convex duality classification theory of over 25 years ago for recent computational complexity results developed for recognizing some of the asymptotic duality states that prevail for an arbitrary convex programming pair. 相似文献
105.
In this paper, we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi-?-nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem. Some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. The results presented in the paper improve and extend some recent results. 相似文献
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研究基于扩展Leslie投影矩阵的离散尺度结构种群模型的最优收获问题,约束条件包括生态平衡和开发成本等.运用凸优化理论证明了最优收获策略的存在性,导出了最优收获模式,应用模型参数给出了收获比率.结论显示:最优策略具有两阶段结构. 相似文献
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Asymptotic synchronization of continuous/discrete complex dynamical networks by optimal partitioning method 下载免费PDF全文
The synchronization problem for both continuous and discrete‐time complex dynamical networks with time‐varying delays is investigated. Using optimal partitioning method, time‐varying delays are partitioned into l subintervals and generalized results are derived in terms of linear matrix inequalities (LMIs). New delay‐dependent synchronization criteria in terms of LMIs are derived by constructing appropriate Lyapunov–Krasovskii functional, reciprocally convex combination technique and some inequality techniques. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2014 Wiley Periodicals, Inc. Complexity 21: 193–210, 2015 相似文献