检索结果-内蒙古大学图书馆

Global optimization for special reverse convex programming

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2008年第6期55卷 1154-1163页

作者： Wang, Yanjun Lan, Ying Shanghai Univ Finance & Econ Dept Appl Math Shanghai 200433 Peoples R China Shanghai Univ Finance & Econ Sch Econ Shanghai 200433 Peoples R China

A global optimization algorithm is proposed in order to locate the global minimum of the special reverse convex programming which is both nonconvex and nonlinear. Three new strategies are adopted in this paper. Some of them can be used to solve general reverse convex programming. Global solution locating is to identify the location of the Solution. The linear relaxation method is used to obtain the lower bound of the optimum of the primal programming, and in this paper the relaxed programming is a kind of linear programming, which can be solved by standard simplex algorithm. The final strategy is upper bound updating method, which provides a better upper bound than the standard branch and bound method. According to the strategies, a global optimization algorithm is derived based on branch and bound theory. It is proved that the algorithm possesses global convergence. Finally, a numerical experiment is given to illustrate the feasibility and the smaller computational effort. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： global optimization reverse convex programming linear relaxation programming branch and bound

来源：评论

学校读者我要写书评

暂无评论

A nonisolated optimal solution for special reverse convex programming problems

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期224卷 219-229页

作者： Shen, Pei-Ping Chen, Yong-Qiang Ma, Yuan Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Peoples R China

In this paper, an efficient algorithm is proposed for globally solving special reverse convex programming problems with more than one reverse convex constraints. The proposed algorithm provides a nonisolated global optimal solution which is also stable under small perturbations of the constraints, and it turns out that such an optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and the numerical experiment is given to illustrate the feasibility of the presented algorithm. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Global optimization reverse convex programming Nonisolated optimal solution Monotonic optimization

来源：评论

学校读者我要写书评

暂无评论

Solving reverse convex programming Problems Using a Generalized Cutting-Plane Method

引用

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE 2019年第A4期43卷 1893-1904页

作者： Sadeghi, J. Mohebi, H. Kerman Grad Univ Adv Technol Dept Math Kerman Iran Shahid Bahonar Univ Kerman Dept Math Kerman *** Iran Shahid Bahonar Univ Kerman Mahani Math Res Ctr Kerman *** Iran

It is well known that each convex function f:Rn?R is supremally generated by affine functions. More precisely, each convex function f:Rn?R is the upper envelope of its affine minorants. In this paper, we propose an algorithm for solving reverse convex programming problems by using such a representation together with a generalized cutting-plane method. Indeed, by applying this representation, we solve a sequence of problems with a smaller feasible set, in which the reverse convex constraint is replaced by a still reverse convex but polyhedral constraint. Moreover, we prove that the proposed algorithm converges, under suitable assumptions, to an optimal solution of the original problem. This algorithm is coded in MATLAB language and is evaluated by some numerical examples.

关键词： Non-convex optimization Generalized cutting-plane method Nonlinear programming reverse convex programming convexity 90C26 65K05 90C30

来源：评论

学校读者我要写书评

暂无评论

A reverse convex programming for Beamforming in Cognitive Multicast Transmission

A Reverse Convex Programming for Beamforming in Cognitive Mu...

引用

3rd International Conference on Communications and Electronics

作者： Phan, A. H. Tuan, H. D. Kha, H. H. Ngo, D. T. Univ New South Wales Sch Elect Engn & Telecommun UNSW Sydney NSW 2052 Australia McGill Univ Dept Elect & Comp Engn Montreal PQ Canada

ISBN: (纸本)9781424470587

The cognitive beamforming problems are naturally formulated as indefinite quadratic (nonconvex) optimization programs. The typical methods for solving such optimization problems are to transform them into convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped to obtain solvable SDP relaxed problems and randomization techniques are employed for seeking the feasible solutions to the original nonconvex optimization problems. In many practical cases, these approaches fail to deliver satisfactory solutions, i.e., their solutions are very far from the optimal ones. In contrast, in this paper the rank-one constraints are equivalently expressed as reverse convex constraints and are incorporated into the optimization problems. Then, we propose an efficient iterative algorithm for solving the nonsmooth reverse convex optimization problems. Our simulations show that our proposed approach yields nearly global optimal solutions with much less computational load as compared to the conventional one.

关键词： array signal processing cognitive beamforming problems cognitive multicast transmission cognitive radio convex programming convex semidefinite programs indefinite quadratic optimization iterative algorithm iterative methods multicast communication optimisation randomization techniques reverse convex programming

来源：评论

学校读者我要写书评

暂无评论

SEQUENTIAL convexIFICATION IN reverse convex AND DISJUNCTIVE programming

引用

MATHEMATICAL programming 1989年第3期44卷 337-350页

作者： BALAS, E TAMA, JM TIND, J 1.Management Science Research Group Graduate School of Industrial Administration Carnegie Mellon University 15213 Pittsburgh PA USA

This paper is about a property of certain combinatorial structures, called sequential convexifiability, shown by Balas (1974, 1979) to hold for facial disjunctive programs. Sequential convexifiability means that the convex hull of a nonconvex set defined by a collection of constraints can be generated by imposing the constraints one by one, sequentially, and generating each time the convex hull of the resulting set. Here we extend the class of problems considered to disjunctive programs with infinitely many terms, also known as reverse convex programs, and give necessary and sufficient conditions for the solution sets of such problems to be sequentially convexifiable. We point out important classes of problems in addition to facial disjunctive programs (for instance, reverse convex programs with equations only) for which the conditions are always satisfied. Finally, we give examples of disjunctive programs for which the conditions are violated, and so the procedure breaks down.

关键词： Disjunctive programming reverse convex programming facial disjunctive sets convex hull generation

来源：评论

学校读者我要写书评

暂无评论

convexification and concavification for a general class of global optimization problems

引用

JOURNAL OF GLOBAL OPTIMIZATION 2005年第1期31卷 45-60页

作者： Wu, ZY Bai, FS Zhang, LS Chongqing Normal Univ Dept Math & Comp Sci Chongqing 400047 Peoples R China Shanghai Univ Dept Math Shanghai 200436 Peoples R China Fudan Univ Inst Math Shanghai 200433 Peoples R China

A kind of general convexification and concavification methods is proposed for solving some classes of global optimization problems with certain monotone properties. It is shown that these minimization problems can be transformed into equivalent concave minimization problem or reverse convex programming problem or canonical D.C. programming problem by using the proposed convexification and concavification schemes. The existing algorithms then can be used to find the global solutions of the transformed problems.

关键词： concave minimization DC programming global optimization monotone programming reverse convex programming

来源：评论

学校读者我要写书评

暂无评论

The Discrete Moment Problem with Nonconvex Shape Constraints

引用

OPERATIONS RESEARCH 2021年第1期69卷 279-296页

作者： Chen, Xi He, Simai Jiang, Bo Ryan, Christopher Thomas Zhang, Teng New York Univ Stern Sch Business New York NY 10012 USA Shanghai Univ Finance & Econ Sch Informat Management & Engn Res Inst Interdisciplinary Sci Shanghai 200433 Peoples R China Univ British Columbia UBC Sauder Sch Business Vancouver BC V6T 1Z2 Canada Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with additional shape constraints that guarantee the worst-case distribution is either log-concave (LC), has an increasing failure rate (IFR), or increasing generalized failure rate (IGFR). These classes of shape constraints have not previously been studied in the literature, in part due to their inherent nonconvexities. Nonetheless, these classes are useful in practice, with applications in revenue management, reliability, and inventory control. We characterize the structure of optimal extreme point distributions under these constraints. We show, for example, that an optimal extreme point solution to a moment problem with m moments and LC shape constraints is piecewise geometric with at most m pieces. This optimality structure allows us to design an exact algorithm for computing optimal solutions in a low-dimensional space of parameters. We also leverage this structure to study a robust newsvendor problem with shape constraints and compute optimal solutions.

关键词： robust optimization moment problem shape constraints reverse convex programming

来源：评论

学校读者我要写书评

暂无评论

ON THE USE OF CUTS IN reverse convex-PROGRAMS

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1991年第2期68卷 257-274页

作者： GURLITZ, TR JACOBSEN, SE UNIV CALIF LOS ANGELES DEPT ELECT ENGN LOS ANGELES CA 90024 USA

A cutting plane method, using the idea of Tuy cuts, has been suggested in earlier papers as a possible means of solving reverse convex programs. However, the method is fraught with theoretical and numerical difficulties. Stringent sufficient conditions for convergence in n dimensions are given. However, examples of nonconvergence are given and reasons for this nonconvergence are developed. A result of the discussion is a convergent algorithm which combines the idea of the cutting plane method with vertex enumeration procedures in order to numerically improve upon the edge search procedure of Hillestad.

关键词： NONconvex programming reverse convex programming CUTTING PLANES NONLINEAR programming

来源：评论

学校读者我要写书评

暂无评论

Global Optimization of Relay Placement for Seafloor Optical Wireless Networks

引用

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2021年第3期20卷 1801-1815页

作者： Inoue, Yoshiaki Kodama, Takahiro Kimura, Tomotaka Osaka Univ Grad Sch Engn Dept Informat & Commun Technol Suita Osaka 5650821 Japan Kagawa Univ Fac Engn & Design Takamatsu Kagawa 7610396 Japan Doshisha Univ Fac Sci & Engn Kyotanabe 6100394 Japan

Optical wireless communication is a promising technology for underwater broadband access networks, which are particularly important for high-resolution environmental monitoring applications. This paper focuses on a deep-sea monitoring system, where an underwater optical wireless network is deployed on the seafloor. We model such an optical wireless network as a general queueing network and formulate an optimal relay placement problem, whose objective is to maximize the stability region of the whole system, i.e., the supremum of the traffic volume that the network is capable of accommodating. The formulated optimization problem is further shown to be non-convex, so that its global optimization is non-trivial. In this paper, we develop a global optimization method for this problem and we provide an efficient algorithm to compute an optimal solution. Through numerical evaluations, we show that a significant performance gain can be obtained by using the derived optimal solution.

关键词： Relays Optical sensors Optical fiber networks Monitoring Optimization Optical fiber communication Wireless sensor networks Underwater communication visible light optical network queueing network global optimization reverse convex programming

来源：评论

学校读者我要写书评

暂无评论

CONSTRUCTION OF TEST PROBLEMS FOR A CLASS OF reverse convex-PROGRAMS

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1994年第2期81卷 343-354页

作者： MOSHIRVAZIRI, K UNIV CALIF LOS ANGELES LOS ANGELES CA 90024 USA

A method of constructing test problems with known global solution for a class of reverse convex programs or linear programs with an additional reverse convex constraint is presented. The initial polyhedron is assumed to be a hypercube. The method then systematically generates cuts that slice the cube in such a way that a prespecified global solution on its edge remains intact. The proposed method does not require the solution of linear programs or systems of linear equations as is often required by existing techniques.

关键词： reverse convex programming NONconvex programming NONLINEAR programming LINEAR programming TEST PROBLEMS GLOBAL OPTIMIZATION

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：