检索结果-内蒙古大学图书馆

47th IEEE Conference on Decision and Control

作者： Hu, Tingshu Blanchini, Franco

ISBN: (纸本)9781424431243

Relationship between polyhedral functions and composite quadratic functions is investigated in this paper. The two composite quadratic functions considered are the pointwise maximum of quadratics and the convex hull of quadratics. It is shown that these two composite quadratic functions are universal for robust, possibly constrained, stabilization problems. In particular, a linear differential inclusion is stable (stabilizable with/without constraints) iff it admits a Lyapunov (control Lyapunov) function in these classes. Relationships between the existing stability/stabilization conditions derived from these functions are also investigated. It is shown that a well known stability condition in terms of matrix equalities is equivalent to a stability condition in terms of bilin-ear matrix inequalities (BMIs). Similar conclusions are made about conditions for stabilization of linear differential/difference inclusions and constrained control systems. This investigation provides insight into the relationship between two alternative approaches to various analysis and design problems, making it possible to transform some synthesis problems derived from polyhedral functions into LMI-based optimization problems.

关键词： polyhedral functions composite quadratic functions stability stabilization

来源：评论

学校读者我要写书评

暂无评论

Role of Subgradients in Variational Analysis of polyhedral functions

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第3期200卷 1160-1192页

作者： Hang, Nguyen T. V. Jung, Woosuk Sarabi, Ebrahim Vietnam Acad Sci & Technol Inst Math Hanoi Vietnam Miami Univ Dept Math Oxford OH 45065 USA

Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the second subderivative and subgradient proto-derivative of polyhedral functions, i.e., functions with polyhedral convex epigraphs, we demonstrate that choosing the underlying subgradient, utilized in the definitions of these concepts, from the relative interior of the subdifferential of polyhedral functions ensures stronger second-order variational properties such as strict twice epi-differentiability and strict subgradient proto-differentiability. This allows us to characterize continuous differentiability of the proximal mapping and twice continuous differentiability of the Moreau envelope of polyhedral functions. We close the paper with proving the equivalence of metric regularity and strong metric regularity of a class of generalized equations at their nondegenerate solutions.

关键词： polyhedral functions Reduction lemma Nondegenerate solutions Strict proto-differentiability Strict twice Epi-differentiability Proximal mappings Strong metric regularity

来源：评论

学校读者我要写书评

暂无评论

On global unconstrained minimization of the difference of polyhedral functions

引用

JOURNAL OF GLOBAL OPTIMIZATION 2011年第2期50卷 179-195页

作者： Polyakova, Lyudmila N. St Petersburg State Univ Dept Appl Math & Control Proc St Petersburg 198504 Russia

The problem of finding a global minimizer of the difference of polyhedral functions is considered. By means of conjugate functions, necessary and sufficient conditions for the unboundedness and the boundedness of such functions in R (n) are derived. Using hypodifferentials of polyhedral functions, necessary and sufficient conditions for a global unconstrained minimum on R (n) are proved.

关键词： Difference of convex functions polyhedral functions Hypodifferential Global optimization Conjugate function

来源：评论

学校读者我要写书评

暂无评论

Stability analysis of nonlinear quadratic systems via polyhedral Lyapunov functions

引用

AUTOMATICA 2011年第3期47卷 614-617页

作者： Amato, Francesco Calabrese, Francesco Cosentino, Carlo Merola, Alessio Magna Graecia Univ Catanzaro Sch Comp Sci & Biomed Engn I-88100 Catanzaro Italy MIT SENSEable City Lab Cambridge MA 02139 USA

Quadratic systems play an important role in the modeling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). For such systems it is mandatory not only to determine whether the origin of the state space is locally asymptotically stable, but also to ensure that the operative range is included into the convergence region of the equilibrium. Based on this observation, this paper considers the following problem: given the zero equilibrium point of a nonlinear quadratic system, assumed to be locally asymptotically stable, and a certain polytope in the state space containing the origin, determine whether this polytope belongs to the domain of attraction of the equilibrium. The proposed approach is based on polyhedral Lyapunov functions, rather than on the classical quadratic Lyapunov functions. An example shows that our methodology may return less conservative results than those obtainable with previous approaches. (c) 2010 Elsevier Ltd. All rights reserved.

关键词： Nonlinear systems Quadratic systems Lyapunov stability Domain of attraction polyhedral functions LMIs optimization

来源：评论

学校读者我要写书评

暂无评论

Separation via polyhedral conic functions

Separation via polyhedral conic functions

引用

6th International Conference on Optimization Technques and Applications (ICOTA)

作者： Gasimov, RN Ozturk, G Eskisehir Osmangazi Univ Dept Ind Engn TR-26030 Bademlik Eskisehir Turkey

We consider the problem of discriminating between two finite point sets A and B in the n -dimensional space by using a special type of polyhedral function. An effective finite algorithm for finding a separating function based on iterative solutions of linear programming subproblems is suggested. At each iteration a function whose graph is a polyhedral cone with vertex at a certain point is constructed and the resulting separating function is defined as a point-wise minimum of these functions. It has been shown that arbitrary two finite point disjoint sets can be separated by using this algorithm. An illustrative example is given and an application on classification problems with some real-world data sets has been implemented.

关键词： separability polyhedral functions polyhedral cones polyhedral conic functions classification

来源：评论

学校读者我要写书评

暂无评论

Directional Differentiability, Coexhausters, Codifferentials and polyhedral DC functions

引用

TAIWANESE JOURNAL OF MATHEMATICS 2023年第3期27卷 611-627页

作者： Abbasov, Majid E. St Petersburg State Univ SPbSU 7 9 Univ nab St Petersburg 199034 Russia Russian Acad Sci Inst Problems Mech Engn 61Bolshoj pr VO St Petersburg 199178 Russia

Codifferentials and coexhausters are used to describe nonhomogeneous approximations of a nonsmooth function. Despite the fact that coexhausters are modern generalizations of codifferentials, the theories of these two concepts continue to develop simultaneously. Moreover, codifferentials and coexhausters are strongly connected with DC functions. In this paper we trace analogies between all these objects, and prove the equivalence of the boundedness and optimality conditions described in terms of these notions. This allows one to extend the results derived in terms of one object to the problems stated via the other one. Another contribution of this paper is the study of connection between nonhomogeneous approximations and directional derivatives and formulate optimality conditions in terms of nonhomogeneous approximations.

关键词： codifferentials coexhausters DC functions polyhedral functions constructive nonsmooth analysis

来源：评论

学校读者我要写书评

暂无评论

Separation via polyhedral conic functions

引用

OPTIMIZATION METHODS & SOFTWARE 2006年第4期21卷 527-540页

作者： Gasimov, RN Ozturk, G Eskisehir Osmangazi Univ Dept Ind Engn TR-26030 Bademlik Eskisehir Turkey

关键词： separability polyhedral functions polyhedral cones polyhedral conic functions classification

来源：评论

学校读者我要写书评

暂无评论

MULTISCALE METHODS FOR polyhedral REGULARIZATIONS

引用

SIAM JOURNAL ON OPTIMIZATION 2013年第3期23卷 1424-1456页

作者： Moeller, Michael Burger, Martin Univ Munster Inst Numer & Angew Math D-48149 Munster Germany

In this paper we present the extension and generalization of the adaptive inverse scale space (aISS) method proposed for l(1) regularization in [Math. Comp., 82 (2013), pp. 269-299] to arbitrary polyhedral functions. We will see that the representation of a convex polyhedral function as a finitely generated function allows us to conclude that the inverse scale space flow (the time continuous formulation of the augmented Lagrangian method) can be solved exactly without discretization. We present an algorithm for the computation of such a solution for arbitrary polyhedral functions, analyze its convergence, and interpret the well-known (forward) scale space flow as the inverse scale space flow on the convex conjugate functional, thus including this class of flows in our analysis. A surprising result is the equivalence of the scale space or gradient flow with a standard variational problem. Finally, we give examples of the applications for the aISS algorithm for polyhedral functions, which illustrate that the resulting algorithm can be fast (depending on the finitely generated representation of the polyhedral function) and behaves favorably over classical variational methods in the case of noisy data.

关键词： inverse scale space scale space adaptivity polyhedral functions convex optimization

来源：评论

学校读者我要写书评

暂无评论

Necessary and sufficient conditions for stable conjugate duality

引用

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2006年第9期64卷 1998-2006页

作者： Burachik, RS Jeyakumar, V Wu, ZY Univ Ballarat Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia Univ S Australia Sch Math & Stat Mawson Lakes SA 5095 Australia Univ New S Wales Sch Math Sydney NSW 2052 Australia Chongqing Normal Univ Dept Math & Comp Sci Chongqing 400047 Peoples R China

The conjugate duality, which states that inf(x is an element of X) phi(x, 0)=max(upsilon is an element of Y') - phi*(0, upsilon), whenever a regularity condition on phi is satisfied, is a key result in convex analysis and optimization, where phi: X x Y -> R boolean OR {+infinity} is a convex function, X and Y are Banach spaces, Y' is the continuous dual space of Y and phi* is the Fenchel-Moreau conjugate of phi. In this paper, we establish a necessary and sufficient condition for the stable conjugate duality, inf(x is an element of X) {phi(x, 0) + x*(x)} = max(upsilon is an element of Y') {-phi*(-x*, upsilon)}, for all x* is an element of X' and then obtain a new epigraph regularity condition for the conjugate duality. The regularity condition is shown to be much more general than the popularly known interior-point type conditions. As an easy consequence we present an epigraph closure condition which is necessary and sufficient for a stable Fenchel-Rockafellar duality theorem. In the case where one of the functions involved is a polyhedral convex function, we provide generalized interior-point conditions for the epigraph regularity condition. Moreover, we show that a stable Fenchel's duality for sublinear functions holds whenever a subdifferential sum formula for the functions holds. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： conjugate duality constraint qualifications convex programming polyhedral functions sublinear functions

来源：评论

学校读者我要写书评

暂无评论

Non-conservative matrix inequality conditions for stability/stabilizability of linear differential inclusions

引用

AUTOMATICA 2010年第1期46卷 190-196页

作者： Hu, Tingshu Blanchini, Franco Univ Massachusetts Dept Elect & Comp Engn Lowell MA 01854 USA Univ Udine Dipartimento Matemat & Informat I-33100 Udine Italy

This paper shows that the matrix inequality conditions for stability/stabilizability of linear differential inclusions derived from two classes of composite quadratic functions are not conservative. It is established that the existing stability/stabilizability conditions by means of polyhedral functions and based on matrix equalities are equivalent to the matrix inequality conditions. This implies that the composite quadratic functions are universal for robust, possibly constrained, stabilization problems of linear differential inclusions. In particular, a linear differential inclusion is stable (stabilizable with/without constraints) iff it admits a Lyapunov (control Lyapunov) function in these classes. Examples demonstrate that the polyhedral functions can be much more complex than the composite quadratic functions, to confirm the stability/stabilizability of the same system. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： polyhedral functions Composite quadratic functions Stability Stabilization

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：