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FUNCTION-SPACE quasi-newton algorithms FOR OPTIMAL-CONTROL PROBLEMS WITH BOUNDED CONTROLS AND SINGULAR ARCS

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1976年第4期20卷 455-479页

作者： EDGE, ER POWERS, WF TRW SYST GRP REDONDO BEACHCA 90278 UNIV MICHIGAN DEPT AEROSP ENGNANN ARBORMI 48104

Two existing function-space quasi-newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-newton methods is shown to be superior to the integral kernel representation. The quasi-newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.

关键词： Optimal control numerical methods computing methods gradient methods quasi-newton algorithms bounded control problems singular arcs

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IMPROVED HYBRID DEMOSAICING AND COLOR SUPER-RESOLUTION IMPLEMENTATION USING quasi-newton algorithms

IMPROVED HYBRID DEMOSAICING AND COLOR SUPER-RESOLUTION IMPLE...

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22nd IEEE Canadian Conference on Electrical and Computer Engineering

作者： Sorrentino, Diego A. Antoniou, Andreas Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P8 Canada

ISBN: (纸本)9781424435098

Super-resolution algorithms can be used to reconstruct a high-resolution high-quality image from a set of low-quality images. A novel hybrid demosaicing and color super-resolution approach proposed recently by Farsiu, Elad, and Milanfar relies on the minimization of a nonconvex multiterm objective function using a rudimentary fixed step-size steepest-descent approach. In this paper, we show that improved performance can be achieved by implementing this approach in terms of powerful quasi-newton algorithms.

关键词： Image processing super-resolution demosaicing quasi-newton algorithms

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Robust quasi-newton Adaptive Filtering algorithms

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2011年第8期58卷 537-541页

作者： Bhotto, Md. Zulfiquar Ali Antoniou, Andreas Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P6 Canada

Two robust quasi-newton (QN) adaptive filtering algorithms that perform well in impulsive-noise environments are proposed. The new algorithms use an improved estimate of the inverse of the autocorrelation matrix and an improved weight-vector update equation, which lead to improved speed of convergence and steady-state misalignment relative to those achieved in the known QN algorithms. A stability analysis shows that the proposed algorithms are asymptotically stable. The proposed algorithms perform data-selective adaptation, which significantly reduces the amount of computation required. Simulation results presented demonstrate the attractive features of the proposed algorithms.

关键词： Adaptive filters impulsive noise in adaptive filters quasi-newton algorithms robust adaptation algorithms

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QUADRATICALLY AND SUPERLINEARLY CONVERGENT algorithms FOR THE SOLUTION OF INEQUALITY CONSTRAINED MINIMIZATION PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1995年第2期85卷 265-289页

作者： FACCHINEI, F LUCIDI, S Dipartimento di Informatica e Sistemistica Università di Roma-La Sapienza Roma Italy. Dipartimento di Informatica e Sistemistica Università di Roma-La Sapicnza Roma Italy.

In this paper, some newton and quasi-newton algorithms for the solution of inequality constrained minimization problems are considered. All the algorithms described produce sequences {x(k)} converging q-superlinearly to the solution. Furthermore, under mild assumptions, a q-quadratic convergence rate in x is also attained. Other features of these algorithms are that only the solution of linear systems of equations is required at each iteration and that the strict complementarity assumption is never invoked. First, the superlinear or quadratic convergence rate of a newton-like algorithm is proved. Then, a simpler version of this algorithm is studied, and it is shown that it is superlinearly convergent. Finally, quasi-newton versions of the previous algorithms are considered and, provided the sequence defined by the algorithms converges, a characterization of superlinear convergence extending the result of Boggs, Tolle, and Wang is given.

关键词： INEQUALITY CONSTRAINED OPTIMIZATION newton ALGORITHM quasi-newton algorithms SUPERLINEAR CONVERGENCE QUADRATIC CONVERGENCE MULTIPLIER FUNCTIONS STRICT COMPLEMENTARITY

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Improved quasi-newton Adaptive-Filtering Algorithm

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2010年第8期57卷 2109-2118页

作者： Ali, Md Zulfiquar Antoniou, Andreas Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P6 Canada

An improved quasi-newton (QN) algorithm that performs data-selective adaptation is proposed whereby the weight vector and the inverse of the input-signal autocorrelation matrix are updated only when the a priori error exceeds a prespecified error bound. The proposed algorithm also incorporates an improved estimator of the inverse of the autocorrelation matrix. With these modifications, the proposed QN algorithm takes significantly fewer updates to converge and yields a reduced steady-state misalignment relative to a known QN algorithm proposed recently. These features of the proposed QN algorithm are demonstrated through extensive simulations. Simulations also show that the proposed QN algorithm, like the known QN algorithm, is quite robust with respect to roundoff errors introduced in fixed-point implementations.

关键词： Adaptation algorithms adaptive filters convergence speed in adaptation algorithms quasi-newton algorithms steady-state misalignment

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Global convergence of a class of collinear scaling algorithms with inexact line searches on convex functions

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COMPUTING 1999年第2期63卷 145-169页

作者： Ariyawansa, KA Begashaw, N Washington State Univ Dept Pure & Appl Math Pullman WA 99164 USA Clark Atlanta Univ Dept Math Sci Atlanta GA 30314 USA

Ariyawansa [2] has presented a class of collinear scaling algorithms for unconstrained minimization. A certain family of algorithms contained in this class may be considered as an extension of quasi-newton methods with the Broyden family [11] of approximants of the objective function Hessian. Byrd, Nocedal and Yuan [7] have shown that all members except the DFP [11] method of the Broyden convex family of quasi-newton methods with Armijo [1] and Goldstein [12] line search termination criteria are globally and q-superlinearly convergent on uniformly convex functions. Extension of this result to the above class of collinear scaling algorithms of Ariyawansa [2] has been impossible because line search termination criteria for collinear scaling algorithms were not known until recently. Ariyawansa [4] has recently proposed such line search termination criteria. In this paper, we prove an analogue of the result of Byrd, Nocedal and Yuan [7] for the family of collinear scaling algorithms of Ariyawansa [2] with the line search termination criteria of Ariyawansa [4].

关键词： unconstrained minimization quasi-newton algorithms collinear scaling algorithms line search termination criteria global and q-superlinear convergence

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Limited-memory BFGS with displacement aggregation

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MATHEMATICAL PROGRAMMING 2022年第1-2期194卷 121-157页

作者： Berahas, Albert S. Curtis, Frank E. Zhou, Baoyu Lehigh Univ Dept Ind & Syst Engn 200 W Packer Ave Bethlehem PA 18015 USA

A displacement aggregation strategy is proposed for the curvature pairs stored in a limited-memory BFGS (a.k.a. L-BFGS) method such that the resulting (inverse) Hessian approximations are equal to those that would be derived from a full-memory BFGS method. This means that, if a sufficiently large number of pairs are stored, then an optimization algorithm employing the limited-memory method can achieve the same theoretical convergence properties as when full-memory (inverse) Hessian approximations are stored and employed, such as a local superlinear rate of convergence under assumptions that are common for attaining such guarantees. To the best of our knowledge, this is the first work in which a local superlinear convergence rate guarantee is offered by a quasi-newton scheme that does not either store all curvature pairs throughout the entire run of the optimization algorithm or store an explicit (inverse) Hessian approximation. Numerical results are presented to show that displacement aggregation within an adaptive L-BFGS scheme can lead to better performance than standard L-BFGS.

关键词： Nonlinear optimization quasi-newton algorithms Broyden-Fletcher-Goldfarb-Shanno (BFGS) Limited-memory BFGS Superlinear convergence

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Fast neural network learning algorithms for medical applications

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NEURAL COMPUTING & APPLICATIONS 2013年第3-4期23卷 1019-1034页

作者： Azar, Ahmad Taher MUST Fac Engn Comp & Software Engn Dept 6th Of October City Egypt

Measuring the blood urea nitrogen concentration is crucial to evaluate dialysis dose (Kt/V) in patients with renal failure. Although frequent measurement is needed to avoid inadequate dialysis efficiency, artificial intelligence can repeatedly perform the forecasting tasks and may be a satisfactory substitute for laboratory tests. Artificial neural networks represent a promising alternative to classical statistical and mathematical methods to solve multidimensional nonlinear problems. It also represents a promising forecasting application in nephrology. In this study, multilayer perceptron (MLP) neural network with fast learning algorithms is used for the accurate prediction of the post-dialysis blood urea concentration. The capabilities of eight different learning algorithms are studied, and their performances are compared. These algorithms are Levenberg-Marquardt, resilient backpropagation, scaled conjugate gradient, conjugate gradient with Powell-Beale restarts, Polak-Ribiere conjugate gradient and Fletcher-Reeves conjugate gradient algorithms, BFGS quasi-newton, and one-step secant. The results indicated that BFGS quasi-newton and Levenberg-Marquardt algorithm produced the best results. Levenberg-Marquardt algorithm outperformed clearly all the other algorithms in the verification phase and was a very robust algorithm in terms of mean absolute error (MAE), root mean square error (RMSE), Pearson's correlation coefficient () and concordance coefficient (R (C) ). The percentage of MAE and RMSE for Levenberg-Marquardt is 0.27 and 0.32 %, respectively, compared to 0.38 and 0.41 % for BFGS quasi-newton and 0.44 and 0.48 % for resilient backpropagation. MLP-based systems can achieve satisfying results for predicting post-dialysis blood urea concentration and single-pool dialysis dose (sp) Kt/V without the need of a detailed description or formulation of the underlying process in contrast to most of the urea kinetic modeling techniques.

关键词： Multilayer perceptron (MLP) Optimum topology Levenberg-Marquardt (LM) Conjugate gradient algorithms quasi-newton algorithms

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Descentwise inexact proximal algorithms for smooth optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2012年第3期53卷 755-769页

作者： Fuentes, Marc Malick, Jerome Lemarechal, Claude CNRS LJK Grenoble F-38334 Montbonnot St Martin France Inria Rhone Alpes F-38334 Montbonnot St Martin France

The proximal method is a standard regularization approach in optimization. Practical implementations of this algorithm require (i) an algorithm to compute the proximal point, (ii) a rule to stop this algorithm, (iii) an update formula for the proximal parameter. In this work we focus on (ii), when smoothness is present-so that newton-like methods can be used for (i): we aim at giving adequate stopping rules to reach overall efficiency of the method. Roughly speaking, usual rules consist in stopping inner iterations when the current iterate is close to the proximal point. By contrast, we use the standard paradigm of numerical optimization: the basis for our stopping test is a "sufficient" decrease of the objective function, namely a fraction of the ideal decrease. We establish convergence of the algorithm thus obtained and we illustrate it on some ill-conditioned problems. The experiments show that combining the proposed inexact proximal scheme with a standard smooth optimization algorithm improves the numerical behaviour of the latter for those ill-conditioned problems.

关键词： Proximal algorithm quasi-newton algorithms Convex analysis

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Learning algorithms for Quaternion-Valued Neural Networks

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NEURAL PROCESSING LETTERS 2018年第3期47卷 949-973页

作者： Popa, Calin-Adrian Polytech Univ Timisoara Dept Comp & Software Engn Blvd V Parvan 2 Timisoara 300223 Romania

This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-newton, and Levenberg-Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in the real- and complex-valued cases led to the idea of extending them to the quaternion domain, also. Experiments done using the proposed training methods on time series prediction applications showed a significant performance improvement over the quaternion gradient descent algorithm.

关键词： Quaternion-valued neural networks Quickprop Resilient backpropagation Delta-bar-delta SuperSAB Conjugate gradient algorithms Scaled conjugate gradient algorithm quasi-newton algorithms Levenberg-Marquardt algorithm Time series prediction

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