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Global convergence of a filter-trust-region algorithm for solving nonsmooth equations

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2010年第4期87卷 788-796页

作者： Yang, Zhenghao Sun, Wenyu Qi, Liqun Nanjing Normal Univ Sch Math & Comp Sci Nanjing Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we present a new algorithm for solving nonsmooth equations, where the function is locally Lipschitzian. The algorithm attempts to combine the efficiency of filter techniques and the robustness of trust-... 详细信息

关键词： nonsmooth equations trust-region algorithm filter technique global convergence

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An efficient two-step trust-region algorithm for exactly determined consistent systems of nonlinear equations

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2020年 367卷 112470-000页

作者： Bahrami, Somayeh Amini, Keyvan Razi Univ Fac Sci Dept Math Kermanshah Iran

In this paper, we propose a modified two-step trust-region algorithm for solving nonlinear systems. Two-step trust-region algorithms, at every iteration, use a trust-region step and an approximate step by saving the Jacobian matrix to have fewer computations. We introduce a convex combination to modify the trust-region subproblems along with an additional criterion to verify whether the first step is accepted or not. We establish global and quadratic convergence of the algorithm under some mild assumptions. Numerical results show that the modified algorithm is efficient and promising. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Nonlinear systems trust-region algorithm Levenberg-Marquardt algorithm Global and quadratic convergence

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Riemannian Newton and trust-region algorithms for analytic rotation in exploratory factor analysis

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BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY 2021年第1期74卷 139-163页

作者： Liu, Yang Univ Maryland Dept Human Dev & Quantitat Methodol 12308 Benjamin Bldg3942 Campus Dr College Pk MD 20742 USA

In exploratory factor analysis, latent factors and factor loadings are seldom interpretable until analytic rotation is performed. Typically, the rotation problem is solved by numerically searching for an element in the manifold of orthogonal or oblique rotation matrices such that the rotated factor loadings minimize a pre-specified complexity function. The widely used gradient projection (GP) algorithm, although simple to program and able to deal with both orthogonal and oblique rotation, is found to suffer from slow convergence when the number of manifest variables and/or the number of latent factors is large. The present work examines the effectiveness of two Riemannian second-order algorithms, which respectively generalize the well-established truncated Newton and trust-region strategies for unconstrained optimization in Euclidean spaces, in solving the rotation problem. When approaching a local minimum, the second-order algorithms usually converge superlinearly or even quadratically, better than first-order algorithms that only converge linearly. It is further observed in Monte Carlo studies that, compared to the GP algorithm, the Riemannian truncated Newton and trust-region algorithms require not only much fewer iterations but also much less processing time to meet the same convergence criterion, especially in the case of oblique rotation.

关键词： exploratory factor analysis analytic rotation Riemannian optimization matrix manifold truncated Newton algorithm trust-region algorithm conjugate gradient algorithm gradient projection algorithm gradient descent algorithm

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Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2019年第3期74卷 669-701页

作者： Brust, Johannes J. Marcia, Roummel F. Petra, Cosmin G. Argonne Natl Lab Lemont IL 60439 USA Univ Calif Merced Merced CA USA Lawrence Livermore Natl Lab Livermore CA 94550 USA

We propose two limited-memory BFGS (L-BFGS) trust-region methods for large-scale optimization with linear equality constraints. The methods are intended for problems where the number of equality constraints is small. By exploiting the structure of the quasi-Newton compact representation, both proposed methods solve the trust-region subproblems nearly exactly, even for large problems. We derive theoretical global convergence results of the proposed algorithms, and compare their numerical effectiveness and performance on a variety of large-scale problems.

关键词： Linear equality constraints Quasi-Newton L-BFGS trust-region algorithm Compact representation Eigendecomposition Shape-changing norm

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On the use of the energy norm in trust-region and adaptive cubic regularization subproblems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2017年第3期68卷 533-554页

作者： Bergou, E. Diouane, Y. Gratton, S. Univ Paris Saclay MaIAGE INRA F-78350 Jouy En Josas France Univ Toulouse Inst Superr Aeronaut & Espace ISAE SUPAERO F-31055 Toulouse 4 France Univ Toulouse INP ENSEEIHT F-31071 Toulouse 7 France

We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the solution of a so-called "subproblem" in which a trial step is computed by solving an optimization problem involving an approximation of the objective function, called "the model". The latter is supposed to be adequate in a neighborhood of the current iterate. In this paper, we address an important practical question related with the choice of the norm for defining the neighborhood. More precisely, assuming here that the Hessian B of the model is symmetric positive definite, we propose the use of the so-called "energy norm"-defined by vertical bar vertical bar x vertical bar vertical bar(B) = root x(T) B-x for all x is an element of R-n -in both TR and ARC techniques. We show that the use of this norm induces remarkable relations between the trial step of both methods that can be used to obtain efficient practical algorithms. We furthermore consider the use of truncated Krylov subspace methods to obtain an approximate trial step for large scale optimization. Within the energy norm, we obtain line search algorithms along the Newton direction, with a special backtracking strategy and an acceptability condition in the spirit of TR/ARC methods. The new line search algorithm, derived by ARC, enjoys a worst-case iteration complexity of O(is an element of(-3/2)) We show the good potential of the energy norm on a set of numerical experiments.

关键词： Nonlinear optimization Unconstrained optimization trust-region algorithm Adaptive regularized framework using cubics Line search algorithm Energy norm Krylov subspace methods Conjugate gradient

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trust-region optimization of all-pass filter for compensation of ionospheric dispersion effects on wideband GNSS signals

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ADVANCES IN SPACE RESEARCH 2020年第12期66卷 2865-2872页

作者： Guo, Ningyan Yu, Zhibin Kou, Yanhong Lu, Mingquan Tsinghua Univ Dept Elect Engn Beijing Peoples R China Harbin Inst Technol Shenzhen Inst Space Sci & Appl Technol Shenzhen Peoples R China Beihang Univ Sch Elect & Informat Engn Beijing Peoples R China

Ionospheric dispersion causes severe distortions and ranging performance degradations of wideband global navigation satellite system (GNSS) signals. To compensate the non-linear and asymmetrical group delay of the dispersive ionosphere, an all-pass filter in the form cascaded biquad sections was proposed in our previous study. On this basis, this paper develops an optimal delay-equalization all-pass filter by using the trust-region algorithm to construct the desired group delay and improve the fitting accuracy. The simulation results the AltBOC(15,10) signal performance demonstrate that the proposed design is more accurate for distortion compensation and thus more effective for ranging bias mitigation than the previous approach. (c) 2020 COSPAR. Published by Elsevier Ltd. All rights reserved.

关键词： Ionospheric dispersion Wideband Global Navigation Satellite System (GNSS) signals Delay compensation trust-region algorithm All-pass filter

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A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第3期69卷 629-652页

作者： Galli, Leonardo Kanzow, Christian Sciandrone, Marco Univ Florence Dept Informat Engn Via Santa Marta 3 I-50139 Florence Italy Univ Wurzburg Inst Math D-97074 Wurzburg Germany

The generalized Nash equilibrium problem (GNEP) is often difficult to solve by Newton-type methods since the problem tends to have locally nonunique solutions. Here we take an existing trust-region method which is known to be locally fast convergent under a relatively mild error bound condition, and modify this method by a nonmonotone strategy in order to obtain a more reliable and efficient solver. The nonmonotone trust-region method inherits the nice local convergence properties of its monotone counterpart and is also shown to have the same global convergence properties. Numerical results indicate that the nonmonotone trust-region method is significantly better than the monotone version, and is at least competitive to an existing software applied to the same reformulation used within our trust-region framework. Additional tests on quasi-variational inequalities (QVI) are also presented to validate efficiency of the proposed extension.

关键词： Generalized Nash equilibrium problem trust-region algorithm Nonmonotone strategy Global convergence Local superlinear convergence Quasi-variational inequalities

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Using surrogate models for efficient optimization of simulated moving bed chromatography

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COMPUTERS & CHEMICAL ENGINEERING 2014年 67卷 121-132页

作者： Li, Suzhou Feng, Lihong Benner, Peter Seidel-Morgenstern, Andreas Max Planck Inst Dynam Complex Tech Syst D-39106 Magdeburg Germany Tech Univ Chemnitz Dept Math D-09126 Chemnitz Germany Otto von Guericke Univ Chair Chem Proc Engn D-39106 Magdeburg Germany

A new approach of using computationally cheap surrogate models for efficient optimization of simulated moving bed (SMB) chromatography is presented. Two different types of surrogate models are developed to replace the detailed but expensive full-order SMB model for optimization purposes. The first type of surrogate is built through a coarse spatial discretization of the first-principles process model. The second one falls into the category of reduced-order modeling. The proper orthogonal decomposition (POD) method is employed to derive cost-efficient reduced-order models (ROMs) for the SMB process. The trust-region optimization framework is proposed to implement an efficient and reliable management of both types of surrogates. The framework restricts the amount of optimization performed with one surrogate and provides an adaptive model update mechanism during the course of optimization. The convergence to an optimum of the original optimization problem can be guaranteed with the help of this model management method. The potential of the new surrogate-based solution algorithm is evaluated by examining a separation problem characterized by nonlinear bi-Langmuir adsorption isotherms. By addressing the feed throughput maximization problem, the performance of each surrogate is compared to that of the standard full-order model based approach in terms of solution accuracy, CPU time and number of iterations. The quantitative results prove that the proposed scheme not only converges to the optimum obtained with the full-order system, but also provides significant computational advantages. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Simulated moving bed (SMB) chromatography Surrogate models Reduced-order modeling trust-region algorithm Optimization

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Using LDA with on-line experiment methods for coping with changes in MIMO dynamic model

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第1期38卷 983-989页

作者： Jen, Chih-Hung Lin, Kuo-Ping Wen, Wu Chou, Chang-Chien Lung Hwa Univ Sci & Technol Dept Informat Management Tao Yuan 333 Taiwan

Many semiconductor processes have the major problem that die-level signature profiles often look completely different on different devices. During 'in-parallel' and 'in-series' manufacturing control procedures, equipment frequently suffer ageing and tool-wearing effects that induce control model changes and generate unstable control. Therefore, if a control system does not compensate for this variation, the next device will not carry out the required follow-up process control. To solve this problem, we propose a novel control framework that integrates the concepts of self-tuning control, on-line experiments, and linear discriminant analysis (LDA). In this paper, LDA with self-tuning control is used to evaluate process changes and adjust the process recipe. When the system determines that the process has generated a large change, the system applies the design-of-experiment concept continuously to collect process data over an expanded experimental range and uses these data with the least squares error (LSE) method to estimate new model parameters. The proposed control strategy then uses the minimized-total-cost principle and applies a trust-region algorithm to obtain a recipe for the next period. Simulation studies show that the proposed system is able to satisfy the control requirement precisely. Finally, a relevant semiconductor multiple-input multiple-output (MIMO) model is used to illustrate the necessary control procedure for verifying the practicability of the proposed system in a MIMO dynamic process. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Self-tuning control On-line experiment Linear discriminant analysis (LDA) trust-region algorithm Multiple-input multiple-output (MIMO) model

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A computationally efficient simulation-based optimization method with region-wise surrogate modeling for stochastic inventory management of supply chains with general network structures

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COMPUTERS & CHEMICAL ENGINEERING 2016年 87卷 164-179页

作者： Ye, Wenhe You, Fengqi Northwestern Univ Dept Chem & Biol Engn Evanston IL 60208 USA

Simulation-based optimization is widely used to improve the performance of an inventory system under uncertainty. However, the black-box function between the input and output, along with the expensive simulation to reproduce a real inventory system, introduces a huge challenge in optimizing these performances. We propose an efficient framework for reducing the total operation cost while satisfying the service level constraints. The performances of each inventory in the system are estimated by kriging models in a region-wise manner which greatly reduces the computational time during both sampling and optimization. The aggregated surrogate models are optimized by a trust-region framework where a model recalibration process is used to ensure the solution's validity. The proposed framework is able to solve general supply chain problems with the multi-sourcing capability, asynchronous ordering, uncertain demand and stochastic lead time. This framework is demonstrated by two case studies with up to 18 nodes with inventory holding capability in the network. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Simulation-based optimization Inventory management trust-region algorithm Surrogate modeling Kriging

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