检索结果-内蒙古大学图书馆

DIRECTIONAL-DERIVATIVES OF optimal value-functions IN MATHEMATICAL-PROGRAMMING

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1994年第2期82卷 397-404页

作者： WANG, CY ZHAO, F RUTGERS STATE UNIV RUTCORNEW BRUNSWICKNJ 08903

This note discusses the existence of the directional derivatives of the optimal value functions in a class of nonlinear programming problems and gives the expressions of the directional derivatives. In the study, it is not assumed that the optimal set at the point discussed is not empty. Many well-known results of this area can be derived as special cases of the main theorems of this note.

关键词： optimal value functions CHARACTERISTIC functions DIRECTIONAL DERIVATIVES

来源：评论

学校读者我要写书评

暂无评论

Subdifferentials of optimal value functions under metric qualification conditions

引用

JOURNAL OF GLOBAL OPTIMIZATION 2024年第1期88卷 253-283页

作者： Huong, Vu Thi An, Duong Thi Viet Xu, Hong-Kun Hangzhou Dianzi Univ Sch Management Hangzhou 310018 Peoples R China Vietnam Acad Sci & Technol Inst Math Hanoi 10072 Vietnam Thai Nguyen Univ Sci Dept Math & Informat Thai Nguyen 250000 Vietnam Hangzhou Dianzi Univ Sch Sci Hangzhou 310018 Peoples R China Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Henan Peoples R China

In this paper, by revisiting intersection rules for normal cones, we give formulas for estimating or computing the Frechet/Mordukhovich/Moreau-Rockafellar subdifferentials of optimal value functions of constrained parametric optimization problems under metric qualification conditions. The results are then applied to derive chain rules for composite functions in both convex and nonconvex situations. Illustrative examples and comparisons to existing results, including those of Mordukhovich and Shao (Trans Amer Math Soc 348:1235-1280, 1996), Mordukhovich et al. (Math Program Ser B 116:369-396, 2009) and of An and Jourani (J Optim Theory Appl 192:82-96, 2022), are also addressed.

关键词： optimal value functions Metric qualification conditions Normal cones Intersection rules Subdifferentials Chain rules

来源：评论

学校读者我要写书评

暂无评论

Coincidence Points of Parameterized Generalized Equations with Applications to optimal value functions

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第1期196卷 177-198页

作者： Arutyunov, Aram V. V. Mordukhovich, Boris S. S. Zhukovskiy, Sergey E. E. Russian Acad Sci VA Trapeznikov Inst Control Sci Moscow Russia Wayne State Univ Dept Math Detroit MI 48202 USA

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of solutions of parameterized generalized equations, implicit function and fixed-point theorems, optimal value functions in parametric optimization, etc. Using the advanced machinery of variational analysis and generalized differentiation that furnishes complete characterizations of well-posedness properties of multifunctions, we establish a general theorem ensuring the existence of parameter-dependent coincidence point mappings with explicit error bounds for parameterized multifunctions between infinite-dimensional spaces. The obtained major result yields a new implicit function theorem and allows us to derive efficient conditions for semicontinuity and continuity of optimal value functions associated with parametric minimization problems subject to constraints governed by parameterized generalized equations.

关键词： Variational analysis and generalized differentiation Parametric optimization Generalized equations Coincidence and implicit function theorems optimal value functions

来源：评论

学校读者我要写书评

暂无评论

GEOMETRY OF optimal value-functions WITH APPLICATIONS TO REDUNDANCY IN LINEAR-PROGRAMMING

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1994年第1期81卷 35-52页

作者： DULA, JH Department of Computer Science and Engineering Southern Methodist University Dallas

In 1967, Wets and Witzgall (Ref. 1) made, in passing, a connection between frames of polyhedral cones and redundancy in linear programming. The present work elaborates and formalizes the theoretical details needed to establish this relation. We study the properties of optimal value functions in order to derive the correspondence between problems in redundancy and the frame of a polyhedral cone. The insights obtained lead to schemes to improve the efficiency of procedures to detect redundancy in the areas of linear programming, stochastic programming, and computational geometry.

关键词： LINEAR PROGRAMMING optimal value functions REDUNDANCY IN LINEAR PROGRAMMING CONVEX HULL PROBLEM DATA ENVELOPMENT ANALYSIS

来源：评论

学校读者我要写书评

暂无评论

On the rate of convergence of infinite horizon discounted optimal value functions

引用

Nonlinear Analysis: Real World Applications 2000年第4期1卷 499-515页

作者： Grüne, Lars Wirth, Fabian J.W. Goethe-Universität FB Mathematik D-60054 Frankfurt AG 1.1 Postfach 11 19 32 Germany Universität Bremen Zentrum für Technomathematik D-28334 Bremen Postfach 330 440 Germany Dipartimento di Matematica Univ. Roma La Sapienza Roma Italy

In this paper we investigate the rate of convergence of the optimal value function of an infinite horizon discounted optimal control problem as the discount rate tends to zero. Using the Integration Theorem for Laplace transformations we provide conditions on averaged functionals along suitable trajectories yielding quadratic pointwise convergence. From this we derive under appropriate controllability conditions criteria for linear uniform convergence of the value functions on control sets. Applications of these results are given and an example is discussed in which both linear and slower rates of convergence occur depending on the cost functional. © 2000 Elsevier Science Ltd. All rights reserved.

关键词： Discount rate Nonlinear optimal control optimal value functions Rate of convergence

来源：评论

学校读者我要写书评

暂无评论

VARIATIONAL PROPERTIES OF value functions

引用

SIAM JOURNAL ON OPTIMIZATION 2013年第3期23卷 1689-1717页

作者： Aravkin, Aleksandr Y. Burke, James V. Friedlander, Michael P. IBM Corp Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA Univ Washington Dept Math Seattle WA 98195 USA Univ British Columbia Dept Comp Sci Vancouver BC V6T 1Z4 Canada

Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters and their effect on the solution and on the optimal value of the optimization problem. The sensitivity of the value function to the regularization parameter can be linked directly to the Lagrange multipliers. This paper characterizes the variational properties of the value functions for a broad class of convex formulations, which are not all covered by standard Lagrange multiplier theory. An inverse function theorem is given that links the value functions of different regularization formulations (not necessarily convex). These results have implications for the selection of regularization parameters, and the development of specialized algorithms. Numerical examples illustrate the theoretical results.

关键词： convex optimization optimal value functions Lagrange multipliers inverse problems

来源：评论

学校读者我要写书评

暂无评论

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

引用

SYSTEMS & CONTROL LETTERS 2014年 72卷 14-21页

作者： Boccia, Andrea Gruene, Lars Worthmann, Karl Univ London Imperial Coll Sci Technol & Med Control & Power Grp London SW7 2AZ England Univ Bayreuth Math Inst D-95440 Bayreuth Germany Tech Univ Ilmenau Inst Math D-98693 Ilmenau Germany

In this paper we investigate stability and recursive feasibility of a nonlinear receding horizon control scheme without terminal constraints and costs but imposing state and control constraints. Under a local controllability assumption we show that every level set of the infinite horizon optimal value function is contained in the basin of attraction of the asymptotically stable equilibrium for sufficiently large optimization horizon N. For stabilizable linear systems we show the same for any compact subset of the interior of the viability kernel. Moreover, estimates for the necessary horizon length N are given via an analysis of the optimal value function at the boundary of the viability kernel. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Predictive control optimal control Nonlinear control Linear systems Stability State constraints Feasibility optimal value functions

来源：评论

学校读者我要写书评

暂无评论

Variational Geometric Approach to Generalized Differential and Conjugate Calculi in Convex Analysis

引用

SET-valueD AND VARIATIONAL ANALYSIS 2017年第4期25卷 731-755页

作者： Mordukhovich, B. S. Nam, N. M. Rector, R. B. Tran, T. Wayne State Univ Dept Math Detroit MI 48202 USA RUDN Univ Moscow 117198 Russia Portland State Univ Fariborz Maseeh Dept Math & Stat Portland OR 97207 USA

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes.

关键词： Convex and variational analysis Fenchel conjugates Normals and subgradients Coderivatives Convex calculus optimal value functions

来源：评论

学校读者我要写书评

暂无评论

Differential Stability of Discrete optimal Control Problems with Possibly Nondifferentiable Costs

引用

APPLIED MATHEMATICS AND OPTIMIZATION 2022年第3期86卷 1-32页

作者： An, D. T., V Huong, V. T. Xu, H. K. Hangzhou Dianzi Univ Sch Management Hangzhou 310018 Peoples R China Thai Nguyen Univ Sci Dept Math & Informat Thai Nguyen 25000 Vietnam Vietnam Acad Sci & Technol Inst Math Hanoi 10072 Vietnam Hangzhou Dianzi Univ Sch Sci Hangzhou 310018 Peoples R China Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Henan Peoples R China

In this paper, a family of discrete optimal control problems that depend on parameters is considered. The control problems are reformulated as parametric optimization problems. By establishing/exploiting abstract results on subdifferentials of optimal value functions of parametric optimization problems, we derive formulas for estimating/computing subdifferentials of optimal value functions of parametric discrete optimal control problems in both nonconvex and convex cases. Namely, for control problems with nonconvex costs, upper-evaluations on the regular subdifferential and the limiting (Mordukhovich) subdifferential of the optimal value function are obtained without using the (strict) differentiability of the costs. Meanwhile, for control problems with convex costs, besides results on estimating/computing the subdifferential (in the sense of convex analysis) of the optimal value function, it is worth pointing out that some properties of the optimal value function are first discussed in this paper.

关键词： Parametric discrete optimal control problems optimal value functions Nondifferentiable costs Linear-convex constraint maps Subdifferentials

来源：评论

学校读者我要写书评

暂无评论

Stability of the solution set of perturbed nonsmooth inequality systems and application

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1997年第1期93卷 199-225页

作者： Yen, ND Institute of Mathematics National Center for Natural Science and Technology Hanoi Vietnam

Stability properties of the solution set of generalized inequality systems with locally Lipschitz functions are obtained under a regularity condition on the generalized Jacobian and the Clarke tangent cone. From these results, we derive sufficient conditions for the optimal value function in a nonsmooth optimization problem to be continuous or locally Lipschitz at a given parameter.

关键词： generalized inequality systems locally Lipschitz vector-valued functions generalized Jacobians optimal value functions

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：