检索结果-内蒙古大学图书馆

Maximizing a concave function over the efficient or weakly-efficient set

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1999年第2期117卷 239-252页

作者： Horst, R Thoai, NV Univ Trier Dept Math D-54286 Trier Germany

An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： multiple criteria analysis optimization over efficient/weakly-effcient sets nonconvex programming global optimization branch and bound

来源：评论

学校读者我要写书评

暂无评论

On concave constraint functions and duality in predominantly black-and-white topology optimization

引用

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2010年第33-36期199卷 2224-2234页

作者： Wood, Derren W. Groenwold, Albert A. Univ Stellenbosch Dept Mech Engn ZA-7600 Stellenbosch South Africa

We study the 'classical' discrete, solid-void or black-and-white topology optimization problem, in which minimum compliance is sought, subject to constraints on the available material resource. We assume that this problem is solved using methods that relax the discreteness requirements during intermediate steps, and that the associated programming problems are solved using sequential approximate optimization (SAO) algorithms based on duality. More specifically, we assume that the advantages of the well-known Falk dual are exploited. Such algorithms represent the state-of-the-art in (large-scale) topology optimization when multiple constraints are present: an important example being the method of moving asymptotes (MMA). We depart by noting that the aforementioned SAO algorithms are invariably formulated using strictly convex subproblems. We then numerically illustrate that strictly concave constraint functions, like those present in volumetric penalization, as recently proposed by Bruns and co-workers, may increase the difficulty of the topology optimization problem when strictly convex approximations are used in the SAO algorithm. In turn, volumetric penalization methods are of notable importance, since they seem to hold much promise for generating predominantly solid-void or discrete designs. We then argue that the nonconvex problems we study may in some instances efficiently be solved using dual SAO methods based on nonconvex (strictly concave) approximations which exhibit monotonicity with respect to the design variables. Indeed, for the topology problem resulting from SIMP-like volumetric penalization, we show explicitly that convex approximations are not necessary. Even though the volumetric penalization constraint is strictly concave, the maximum of the resulting dual subproblem still corresponds to the optimum of the original primal approximate subproblem. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Topology optimization SIMP Volumetric penalization Sequential approximate optimization (SAO) nonconvex programming Falk dual

来源：评论

学校读者我要写书评

暂无评论

Subspace-Modeling-Based Nonlinear Measurement for Process Design

引用

INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2011年第23期50卷 13457-13465页

作者： Lu, XinJiang Huang, MingHui Li, YiBo Chen, Min Cent S Univ State Key Lab High Performance Complex Mfg Changsha 410083 Hunan Peoples R China

In industry, many nonlinear processes can be approximated well by a linear model under a suitable design parameter, upon which a linear controller can effectively control these processes. The key problem is how to find this suitable design parameter, which is never considered in process design. In this paper, a novel design for control approach is proposed to design the process to have a satisfactory linear approximation. First, a subspace-modeling-based nonlinear measurement is proposed to avoid the infinite dimensional optimization problem in the traditional nonlinearity measurement. Then a particle-swarm-optimization-based design approach is developed to obtain the optimal design parameter through solving the nonconvex and nondifferential measurement problem. Finally, the proposed design is applied to design a practical curing oven and compared with the existing design.

关键词： PARTICLE swarm optimization MATHEMATICAL models MATHEMATICAL optimization EXPERIMENTAL design PROBLEM solving nonconvex programming NONLINEAR programming

来源：评论

学校读者我要写书评

暂无评论

ON THE CONVERGENCE OF MIRROR DESCENT BEYOND STOCHASTIC CONVEX programming

引用

SIAM JOURNAL ON OPTIMIZATION 2020年第1期30卷 687-716页

作者： Zhou, Zhengyuan Mertikopoulos, Panayotis Bambos, Nicholas Boyd, Stephen P. Glynn, Peter W. IBM Res Yorktown Hts NY 10598 USA NYU Stern Sch Business 550 1St Ave New York NY 10012 USA Univ Grenoble Alpes CNRS Grenoble INP InriaLIG F-38000 Grenoble France Stanford Univ Dept Elect Engn Dept Management Sci & Engn Stanford CA 94305 USA

In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex) and which we call variationally coherent. Since the standard technique of "ergodic averaging" offers no tangible benefits beyond convex programming, we focus directly on the algorithm's last generated sample (its "last iterate"), and we show that it converges with probabiility 1 if the underlying problem is coherent. We further consider a localized version of variational coherence which ensures local convergence of Stochastic mirror descent (SMD) with high probability. These results contribute to the landscape of nonconvex stochastic optimization by showing that (quasi-)convexity is not essential for convergence to a global minimum: rather, variational coherence, a much weaker requirement, suffices. Finally, building on the above, we reveal an interesting insight regarding the convergence speed of SMD: in problems with sharp minima (such as generic linear programs or concave minimization problems), SMD reaches a minimum point in a finite number of steps (a.s.), even in the presence of persistent gradient noise. This result is to be contrasted with existing black-box convergence rate estimates that are only asymptotic.

关键词： mirror descent nonconvex programming stochastic optimization stochastic approximation variational coherence

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

DC programming: Overview

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第1期103卷 1-43页

作者： Horst, R Thoai, NV Univ Trier Dept Math Trier Germany

Mathematical programming problems dealing with functions, each of which can be represented as a difference of two convex functions, are called DC programming problems. The purpose of this overview is to discuss main theoretical results, some applications, and solution methods for this interesting and important class of programming problems. Some modifications and new results on the optimality conditions and development of algorithms are also presented.

关键词： DC functions DC programming global optimization nonconvex programming optimality conditions

来源：评论

学校读者我要写书评

暂无评论

A note on the complexity of L_p minimization

引用

MATHEMATICAL programming 2011年第2期129卷 285-299页

作者： Ge, Dongdong Jiang, Xiaoye Ye, Yinyu Shanghai Jiao Tong Univ Antai Sch Econ & Management Shanghai 200052 Peoples R China Stanford Univ Inst Computat & Math Engn Stanford CA 94305 USA Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

We discuss the L-p (0 <= p < 1) minimization problem arising from sparse solution construction and compressed sensing. For any fixed 0 < p < 1, we prove that finding the global minimal value of the problem is strongly NP-Hard, but computing a local minimizer of the problem can be done in polynomial time. We also develop an interior-point potential reduction algorithm with a provable complexity bound and demonstrate preliminary computational results of effectiveness of the algorithm.

关键词： nonconvex programming Global optimization Interior-point method Sparse solution reconstruction

来源：评论

学校读者我要写书评

暂无评论

Multiple Flat Projections for Cross-Manifold Clustering

引用

IEEE TRANSACTIONS ON CYBERNETICS 2022年第8期52卷 7704-7718页

作者： Bai, Lan Shao, Yuan-Hai Wang, Zhen Chen, Wei-Jie Deng, Nai-Yang Inner Mongolia Univ Sch Math Sci Hohhot 010021 Peoples R China Hainan Univ Sch Management Haikou 570228 Hainan Peoples R China Jilin Univ Minist Educ Key Lab Symbol Computat & Knowledge Engn Changchun 130012 Peoples R China Zhejiang Univ Technol Zhijiang Coll Hangzhou 310014 Peoples R China China Agr Univ Coll Sci Beijing 100083 Peoples R China

Cross-manifold clustering is an extreme challenge learning problem. Since the low-density hypothesis is not satisfied in cross-manifold problems, many traditional clustering methods failed to discover the cross-manifold structures. In this article, we propose multiple flat projections clustering (MFPC) for cross-manifold clustering. In our MFPC, the given samples are projected into multiple localized flats to discover the global structures of implicit manifolds. Thus, the intersected clusters are distinguished in various projection flats. In MFPC, a series of nonconvex matrix optimization problems is solved by a proposed recursive algorithm. Furthermore, a nonlinear version of MFPC is extended via kernel tricks to deal with a more complex cross-manifold learning situation. The synthetic tests show that our MFPC works on the cross-manifold structures well. Moreover, experimental results on the benchmark datasets and object tracking videos show excellent performance of our MFPC compared with some state-of-the-art manifold clustering methods.

关键词： Manifolds Clustering methods Support vector machines Periodic structures Optimization Indexes Elongation Clustering cross-manifold clustering flat-based clustering manifold clustering nonconvex programming

来源：评论

学校读者我要写书评

暂无评论

A FINITE, NONADJACENT EXTREME-POINT SEARCH ALGORITHM FOR OPTIMIZATION OVER THE EFFICIENT SET

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1992年第1期73卷 47-64页

作者： BENSON, HP UNIV FLORIDA COLL BUSINESS ADMGAINESVILLEFL 32611 USA

The problem (P) of optimizing a linear function over the efficient set of a multiple-objective linear program serves many useful purposes in multiple-criteria decision making. Mathematically, problem (P) can be classified as a global optimization problem. Such problems are much more difficult to solve than convex programming problems. In this paper, a nonadjacent extreme-point search algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact extreme-point optimal solution for the problem after a finite number of iterations. It can be implemented using only linear programming methods. Convergence of the algorithm is proven, and a discussion is included of its main advantages and disadvantages.

关键词： MULTIPLE-CRITERIA DECISION MAKING EXTREME-POINT SEARCH GLOBAL OPTIMIZATION EFFICIENT SET nonconvex programming

来源：评论

学校读者我要写书评

暂无评论

Self-adaptive algorithms for quasiconvex programming and applications to machine learning

引用

COMPUTATIONAL & APPLIED MATHEMATICS 2024年第4期43卷 1-16页

作者： Thang, Tran Ngoc Hai, Trinh Ngoc Hanoi Univ Sci & Technol Sch Appl Math & Informat Hanoi Vietnam

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach under mild assumptions. Specifically, the objective function may not satisfy the convexity condition. Unlike descent line-search algorithms, it does not need a known Lipschitz constant to figure out how big the first step should be. The crucial feature of this process is the steady reduction of the step size until a certain condition is fulfilled. In particular, it can provide a new gradient projection approach to optimization problems with an unbounded constrained set. To demonstrate the effectiveness of the proposed technique for large-scale problems, we apply it to some experiments on machine learning, such as supervised feature selection, multi-variable logistic regressions and neural networks for classification.

关键词： nonconvex programming Gradient descent algorithms Quasiconvex functions Pseudoconvex functions Self-adaptive step-sizes

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：