检索结果-内蒙古大学图书馆

On the complexity of finding first-order critical points in constrained nonlinear optimization

MATHEMATICAL PROGRAMMING 2014年第1-2期144卷 93-106页

作者： Cartis, Coralia Gould, Nicholas I. M. Toint, Philippe L. Univ Edinburgh Sch Math Edinburgh EH9 3JZ Midlothian Scotland Rutherford Appleton Lab Computat Sci & Engn Dept Chilton OX11 0QX Oxon England FUNDP Univ Namur Dept Math Namur Ctr Complex Syst NaXys B-5000 Namur Belgium

The complexity of finding -approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that in terms of function and constraints evaluations. This result is obtained by analyzing the worst-case behaviour of a first-order short-step homotopy algorithm consisting of a feasibility phase followed by an optimization phase, and requires minimal assumptions on the objective function. Since a bound of the same order is known to be valid for the unconstrained case, this leads to the conclusion that the presence of possibly nonlinear/nonconvex inequality/equality constraints is irrelevant for this bound to apply.

关键词： Evaluation complexity Worst-case analysis constrained nonlinear optimization

来源：评论

学校读者我要写书评

暂无评论

Fuzzy controllers gains tuning: a constrained nonlinear optimization approach

引用

NEURAL COMPUTING & APPLICATIONS 2013年第3-4期23卷 617-624页

作者： Gil, Paulo Lucena, Catarina Cardoso, Alberto Palma, Luis Univ Nova Lisboa Dept Engn Electrotecn Fac Ciencias & Tecnol P-2829516 Caparica Portugal Univ Coimbra Dept Informat Engn CISUC Ctr Informat & Syst P-3030290 Coimbra Portugal Univ Nova Lisboa Inst Dev New Tecnol P-2829516 Caparica Portugal

This paper presents a methodology for tuning the gains of fuzzy proportional-integral controllers where the concept of closed-loop control system performance is explicitly taken into account. The fuzzy controller gains are found by solving a nonlinear constrained optimization problem considering the system's dynamics described by a nonlinear model and a set of constraints on the controller gains, control actions and outputs. Experimental results collected on a test-bed show the pertinence of using the proposed tuning technique.

关键词： Fuzzy control Scaling factors Gains tuning constrained nonlinear optimization

来源：评论

学校读者我要写书评

暂无评论

On the complexity of finding first-order critical points in constrained nonlinear optimization (vol 144, pg 93, 2014)

引用

MATHEMATICAL PROGRAMMING 2017年第1-2期161卷 611-626页

作者： Cartis, C. Gould, N. I. M. Toint, Ph. L. Univ Oxford Math Inst Woodstock Rd Oxford OX2 6GG England Rutherford Appleton Lab Computat Sci & Engn Dept Chilton OX11 0QX Oxon England FUNDP Univ Namur Namur Ctr Complex Syst naXys 61 Rue Bruxelles B-5000 Namur Belgium FUNDP Univ Namur Dept Math 61 Rue Bruxelles B-5000 Namur Belgium

In a recent paper (Cartis et al. in Math Prog A 144(2):93-106, 2014), the evaluation complexity of an algorithm to find an approximate first-order critical point for the general smooth constrained optimization problem was examined. Unfortunately, the proof of Lemma 3.5 in that paper uses a result from an earlier paper in an incorrect way, and indeed the result of the lemma is false. The purpose of this corrigendum is to provide a modification of the previous analysis that allows us to restore the complexity bound for a different, scaled measure of first-order criticality.

关键词： Evaluation complexity Worst-case analysis constrained nonlinear optimization

来源：评论

学校读者我要写书评

暂无评论

ON THE EVALUATION COMPLEXITY OF CUBIC REGULARIZATION METHODS FOR POTENTIALLY RANK-DEFICIENT nonlinear LEAST-SQUARES PROBLEMS AND ITS RELEVANCE TO constrained nonlinear optimization

引用

SIAM JOURNAL ON optimization 2013年第3期23卷 1553-1574页

作者： Cartis, Coralia Gould, Nicholas I. M. Toint, Philippe L. Univ Edinburgh Sch Math Edinburgh EH9 3JZ Midlothian Scotland Rutherford Appleton Lab Computat Sci & Engn Dept Chilton OX11 0QX Oxon England Univ Namur Namur Ctr Complex Syst NAXyS B-5000 Namur Belgium

We propose a new termination criterion suitable for potentially singular, zero or nonzero residual, least-squares problems, with which cubic regularization variants take at most O(epsilon(-3/2)) residual- and Jacobian-evaluations to drive either the Euclidean norm of the residual or its gradient below epsilon;this is the best known bound for potentially rank-deficient nonlinear least-squares problems. We then apply the new optimality measure and cubic regularization steps to a family of least-squares merit functions in the context of a target-following algorithm for nonlinear equality-constrained problems;this approach yields the first evaluation complexity bound of order epsilon(-3/2) for nonconvexly constrained problems when higher accuracy is required for primal feasibility than for dual first-order criticality.

关键词： evaluation complexity worst-case analysis least-squares problems constrained nonlinear optimization cubic regularization methods

来源：评论

学校读者我要写书评

暂无评论

ON THE EVALUATION COMPLEXITY OF constrained nonlinear LEAST-SQUARES AND GENERAL constrained nonlinear optimization USING SECOND-ORDER METHODS

引用

SIAM JOURNAL ON NUMERICAL ANALYSIS 2015年第2期53卷 836-851页

作者： Cartis, Coralia Gould, Nicholas I. M. Toint, Philippe L. Univ Oxford Math Inst Oxford OX2 6GG England Rutherford Appleton Lab Numer Anal Grp Didcot OX11 0QX Oxon England Univ Namur Namur Ctr Complex Syst naXys B-5000 Namur Belgium Univ Namur Dept Math B-5000 Namur Belgium

When solving the general smooth nonlinear and possibly nonconvex optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy epsilon can be obtained by a second-order method using cubic regularization in at most O(epsilon(-3/2)) evaluations of problem functions, the same order bound as in the unconstrained case. This result is obtained by first showing that the same result holds for inequality constrained nonlinear leastsquares. As a consequence, the presence of (possibly nonconvex) equality/inequality constraints does not affect the complexity of finding approximate first-order critical points in nonconvex optimization. This result improves on the best known (O(epsilon(-2))) evaluation-complexity bound for solving general nonconvexly constrained optimization problems.

关键词： evaluation complexity worst-case analysis least-squares problems constrained nonlinear optimization cubic regularization methods

来源：评论

学校读者我要写书评

暂无评论

Noise-Suppressing Neural Dynamics for Time-Dependent constrained nonlinear optimization With Applications

引用

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第10期52卷 6139-6150页

作者： Wei, Lin Jin, Long Luo, Xin Lanzhou Univ Sch Informat Sci & Engn Lanzhou 730000 Peoples R China Chinese Acad Sci Chongqing Engn Res Ctr Big Data Applicat Smart Ci Chongqing Inst Green & Intelligent Technol Chongqing 400714 Peoples R China Chinese Acad Sci Chongqing Key Lab Big Data & Intelligent Comp Chongqing Inst Green & Intelligent Technol Chongqing 400714 Peoples R China

Up to date, the existing methods for nonlinear optimization with time-dependent parameters can be classified into two types: 1) static methods are capable of handling inequality constraints but may generate large lagging errors in the solution of the intrinsically time-dependent constrained nonlinear optimization (TDCNO) problem due to the hypothesis of short-time invariance and 2) time-variant methods, e.g., zeroing neural networks, are able to remedy the lagging error but fail to solve the TDCNO problem under inequality constraints. To resolve this contradiction, a noise-suppressing neural dynamics (NSND) model is proposed to solve the TDCNO problem subject to both equality and inequality constraints via the nonlinear complementary problem (NCP) function. The proposed method allows inequality constraints for unknown variables, removes the short-time invariance hypothesis, and further eliminates lagging errors during the solving process in the presence of noises. Besides, the rapid convergence, global stability, and noise processing of the NSND model are verified by the theoretical analyses. Simulation results of illustrative examples, including dimensionality reduction on principal component analyses (PCA) and a robot motion control, show that the NSND model outperforms the existing models for the TDCNO problem.

关键词： optimization Mathematical models Analytical models Convergence Principal component analysis Time-varying systems nonlinear equations constrained nonlinear optimization dimensionality reduction on principal component analyses (PCA) equality and inequality constraints neural dynamics noise suppression robot arm control

来源：评论

学校读者我要写书评

暂无评论

A Novel TRUST-TECH-Enabled Trajectory-Unified Methodology for Computing Multiple Optimal Solutions of constrained nonlinear optimization: Theory and Computation

引用

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第1期52卷 473-484页

作者： Zhang, Yong-Feng Chiang, Hsiao-Dong Wang, Tao Univ Jinan Sch Elect Engn Jinan 250022 Peoples R China Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA Natl Supercomp Ctr Guangzhou Guangzhou Peoples R China Sun Yat Sen Univ Sch Data & Comp Sci Guangdong Prov Key Lab Computat Sci Guangzhou 510006 Peoples R China

A novel trajectory-unified (TJU) methodology, enabled by transformation under stability-retraining equilibria characterization (TRUST-TECH, TT) method, is proposed to systematically and deterministically compute a set of multiple local optimal solutions (LOSs), if not all of them, for constrained nonlinear optimization problems. The proposed TT-TJU methodology is composed of two key phases. During Phase I, it robustly computes a LOS;while during Phase II, it systematically computes a set of neighboring LOSs. A theoretical foundation is developed for the proposed TT-TJU methodology. The existence of an optimal solution is shown to be equivalent to the existence of a stable equilibrium point of a class of nonlinear dynamical system derived from the constrained optimization problem under study. From a computational viewpoint, Phase I is numerically implemented in a 3-stage procedure for fast and robust computation of an optimal solution. The second phase makes use of the TRUST-TECH methodology to lead the search away from a computed optimal solution and continue to deterministically compute neighboring LOSs. The proposed methodology has been evaluated on an illustrative bivariate example and a benchmark problem with 110 variables and 55 constraints with promising results.

关键词： optimization Convergence Asymptotic stability nonlinear dynamical systems Linear programming Search problems constrained nonlinear optimization global optimal solution multiple local optimal solutions (LOSs) trajectory-unified (TJU) methodology transformation under stability-retraining equilibria characterization (TRUST-TECH) methodology

来源：评论

学校读者我要写书评

暂无评论

CONSTRUCTING LARGE FEASIBLE SUBOPTIMAL INTERVALS FOR constrained nonlinear optimization

引用

ANNALS OF OPERATIONS RESEARCH 1995年第4期58卷 279-293页

作者： CSENDES, T ZABINSKY, ZB KRISTINSDOTTIR, BP ATTILA JOZSEF UNIV KALMAR LAB H-6701 SZEGED HUNGARY UNIV WASHINGTON IND ENGN PROGRAM SEATTLE WA 98195 USA

An algorithm for finding a large feasible n-dimensional interval for constrained global optimization is presented. The n-dimensional interval is iteratively enlarged about a seed point while maintaining feasibility. An interval subdivision method may be used to check feasibility of the growing box. The resultant feasible interval is constrained to he within a given level set, thus ensuring it is close to the optimum. The ability to determine such a feasible interval is useful for exploring the neighbourhood of the optimum, and can be practically used in manufacturing considerations. The numerical properties of the algorithm are tested and demonstrated by an example problem.

关键词： constrained nonlinear optimization SENSITIVITY ANALYSIS INCLUSION FUNCTION INTERVAL ARITHMETIC

来源：评论

学校读者我要写书评

暂无评论

A Genetic Algorithm and Fuzzy Approach (GAFA) for constrained nonlinear optimization in Design

引用

INTERNATIONAL JOURNAL FOR COMPUTATIONAL METHODS IN ENGINEERING SCIENCE & MECHANICS 2006年第3期7卷 173-189页

作者： Bhuvaneshwaran, Vijayakumar Langari, Reza Temponi, Cecilia Texas A&M Univ Dept Mech Engn College Stn TX 77843 USA Southwest Texas State Univ Coll Business San Marcos TX USA

constrained nonlinear optimization (CNLO) problems often involve imprecise objectives and constraints. The application of conventional nonlinear optimization techniques does not seem the best approach for CNLO. A multi-objective multi-constraint algorithm is proposed in this paper to find an approximation of the so-called pareto-optimal solution, which is searched by a genetic algorithm that uses constraints and objective functions defined via fuzzy sets. The proposed algorithm is illustrated by two classic examples in the field of engineering design. Results indicate that the proposed algorithm is effective in terms of finding a solution that is within acceptable proximity of the so-called pareto-optimal front. Moreover, a comparative analysis of the performance of the proposed approach with those reported in the literature reveals the computational efficiency of the modified algorithm;the population evolves towards the Pareto-optimal set.

关键词： constrained nonlinear optimization Pareto-optimality Genetic Algorithm Fuzzy Logic Engineering Design

来源：评论

学校读者我要写书评

暂无评论

A Trajectory-Based Method for constrained nonlinear optimization Problems

引用

JOURNAL OF optimization THEORY AND APPLICATIONS 2018年第2期177卷 479-497页

作者： Ali, M. Montaz Oliphant, Terry-Leigh Univ Witwatersrand Wits Sch Comp Sci & Appl Math Private Bag 3 ZA-2050 Johannesburg South Africa Univ Witwatersrand Wits TCSE Fac Engn & Built Environm Private Bag 3 ZA-2050 Johannesburg South Africa

A trajectory-based method for solving constrained nonlinear optimization problems is proposed. The method is an extension of a trajectory-based method for unconstrained optimization. The optimization problem is transformed into a system of second-order differential equations with the aid of the augmented Lagrangian. Several novel contributions are made, including a new penalty parameter updating strategy, an adaptive step size routine for numerical integration and a scaling mechanism. A new criterion is suggested for the adjustment of the penalty parameter. Global convergence properties of the method are established.

关键词： Trajectory-based method constrained nonlinear optimization System of ordinary differential equations Numerical integration Convergence

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：