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An approximate and computationally efficient algorithm for computing reference stress for creep life assessment

INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 1998年第6期75卷 459-465页

作者： Zarrabi, K Modarres-Motlagh, A Univ New S Wales Sch Mech & Mfg Engn Sydney NSW 2052 Australia

One of the powerful methods that are currently available for the design and life assessment of components that operate within the creep range is the reference stress (RS) method. However, for problems for which the RS is not available from existing solutions, one usually needs to use a non-linear finite element method which is normally iterative, time-consuming and computationally expensive. An efficient and effective method for computing an approximate value for RS is described that combines a lower-bound theorem and finite element discretization. The resulted quadratic programming is solved by an active set algorithm. The verification and application of the proposed method are also described. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： creep-life assessment reference stress active set algorithm

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A Full Multigrid Method for Linear Complementarity Problems arising from Elastic Normal Contact Problems

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MATHEMATICAL MODELLING AND ANALYSIS 2014年第2期19卷 216-240页

作者： Zhao, Jing Vollebregt, Edwin A. H. Oosterlee, Cornelis W. Delft Univ Technol NL-2628 CD Delft Netherlands VORtech BV NL-2628 CD Delft Netherlands Ctr Math & Comp Sci NL-1090 GB Amsterdam Netherlands

This paper presents a full multigrid (FMG) technique, which combines a multigrid method, an active set algorithm and a nested iteration technique, to solve a linear complementarity problem (LCP) modeling elastic normal contact problems. The governing system in this LCP is derived from a Fredholm integral of the first kind, and its coefficient matrix is dense, symmetric and positive definite. One multigrid cycle is applied to solve this system approximately in each active set iteration. Moreover, this multigrid solver incorporates a special strategy to handle the complementarity conditions, including restricting both the defect and the contact area (active set) to the coarse grid, and setting all quantities outside contact to zero. The smoother is chosen by some analysis based on the eigenvectors of the iteration matrix. This method is applied to a Hertzian smooth contact and a rough surface contact problem.

关键词： full multigrid linear complementarity problems integral equation normal contact problems active set algorithm

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PROJECTION ONTO A POLYHEDRON THAT EXPLOITS SPARSITY

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SIAM JOURNAL ON OPTIMIZATION 2016年第3期26卷 1773-1798页

作者： Hager, William W. Zhang, Hongchao Univ Florida Dept Math Gainesville FL 32611 USA Louisiana State Univ Dept Math Baton Rouge LA 70803 USA

An algorithm is developed for projecting a point onto a polyhedron. The algorithm solves a dual version of the projection problem and then uses the relationship between the primal and dual to recover the projection. The techniques in the paper exploit sparsity. Sparse reconstruction by separable approximation (SpaRSA) is used to approximately identify active constraints in the polyhedron, and the dual active set algorithm (DASA) is used to compute a high precision solution. A linear convergence result is established for SpaRSA that does not require the strong concavity of the dual to the projection problem, and an earlier R-linear convergence rate is strengthened to a Q-linear convergence property. An algorithmic framework is developed for combining SpaRSA with an asymptotically preferred algorithm such as DASA. It is shown that only the preferred algorithm is executed asymptotically. Numerical results are given using the polyhedra associated with the Netlib LP test set. A comparison is made to the interior point method contained in the general purpose open source software package IPOPT for nonlinear optimization, and to the commercial package CPLEX, which contains an implementation of the barrier method that is targeted to problems with the structure of the polyhedral projection problem.

关键词： polyhedral projection SpaRSA active set algorithm dual active set algorithm DASA multilevel optimization

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Design and application of nature inspired computing approach for nonlinear stiff oscillatory problems

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NEURAL COMPUTING & APPLICATIONS 2015年第7期26卷 1763-1780页

作者： Khan, Junaid Ali Raja, Muhammad Asif Zahoor Syam, Muhammed I. Tanoli, Shujaat Ali Khan Awan, Saeed Ehsan Hamdard Univ Fac Engn Sci & Technol Islamabad Pakistan COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan UAE Univ Dept Math Sci Al Ain U Arab Emirates

In this paper, meta-heuristic intelligent approaches are developed for handling nonlinear oscillatory problems with stiff and non-stiff conditions. The mathematical modeling of these oscillators is accomplished using feed-forward artificial neural networks (ANNs) in the form of an unsupervised manner. The accuracy as well as efficiency of the model is subject to the tuning of adaptive parameters for ANNs that are highly stochastic in nature. These optimal weights are carried out with swarm intelligence and pattern search methods hybridized with an efficient local search technique based on constraints minimization known as active set algorithm. The proposed schemes are validated on various stiff and non-stiff variants of the oscillator. The significance, applicability and reliability of the proposed scheme are well established based on comparison made with the results of standard numerical solver.

关键词： Van der Pol oscillators Neural networks Swarm intelligence active set algorithm Pattern search

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Stochastic numerical treatment for solving Troesch's problem

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INFORMATION SCIENCES 2014年 279卷 860-873页

作者： Raja, Muhammad Asif Zahoor COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan Int Islamic Univ Fac Engn & Technol Dept Elect Engn Islamabad Pakistan

In this article, the numerical techniques are presented for the solution of Troesch's problem based on neural networks optimized with three different methods including particle swarm optimization (PSO), active set (AS) and PSO hybridized with AS (PSO-AS) algorithms. The variable transformation is applied in order to convert the original problem to a transformed problem which is relatively less stiff to solve. Feed-forward artificial neural networks are used to model the transformed problem. Learning of adjustable parameters is made with PSO, AS and PSO-AS algorithms. The proposed methodologies are applied to a number of cases for stiff and non-stiff boundary value problems. The comparative analyses are carried out with other standard numerical solutions, as well as approximate analytical solver. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Troesch's problem Non-linear ODE Artificial neural network Particle swarm optimization algorithm active set algorithm Hybrid technique

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Quadratic programming with transaction costs

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COMPUTERS & OPERATIONS RESEARCH 2008年第1期35卷 18-33页

作者： Best, Michael J. Hlouskova, Jaroslava Univ Waterloo Fac Math Dept Combinator & Optimizat Waterloo ON N2L 3G1 Canada Inst Adv Studies Dept Econ & Finance Vienna Austria

We consider the problem of maximizing the mean-variance utility function of n assets. Associated with a change in an asset's holdings from its current or target value is a transaction cost. These must be accounted for in practical problems. A straightforward way of doing so results in a 3n-dimensional optimization problem with 3n additional constraints. This higher dimensional problem is computationally expensive to solve. We present an algorithm for solving the 3n-dimensional problem by modifying an active set quadratic programming (QP) algorithm to solve the 3n-dimensional problem as an n-dimensional problem accounting for the transaction costs implicitly rather than explicitly. The method is based on deriving the optimality conditions for the higher dimensional problem solely in terms of lower dimensional quantities and requires substantially less computational effort than any active set QP algorithm applied directly on a 3n-dimensional problem. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： quadratic programming active set algorithm portfolio optimization transaction costs

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Maximum-likelihood estimation of a log-concave density based on censored data

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ELECTRONIC JOURNAL OF STATISTICS 2014年第1期8卷 1405-1437页

作者： Duembgen, Lutz Rufibach, Kaspar Univ Bern Inst Math Stat & Actuarial Sci CH-3012 Bern Switzerland F Hoffmann La Roche & Cie AG Biostat Oncol CH-4070 Basel Switzerland

We consider nonparametric maximum-likelihood estimation of a log-concave density in case of interval-censored, right-censored and binned data. We allow for the possibility of a subprobability density with an additional mass at +infinity, which is estimated simultaneously. The existence of the estimator is proved under mild conditions and various theoretical aspects are given, such as certain shape and consistency properties. An EM algorithm is proposed for the approximate computation of the estimator and its performance is illustrated in two examples.

关键词： active set algorithm binning cure parameter expectation-maximization algorithm interval-censoring qualitative constraints right-censoring

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Least squares and shrinkage estimation under bimonotonicity constraints

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STATISTICS AND COMPUTING 2010年第2期20卷 177-189页

作者： Beran, Rudolf Duembgen, Lutz Univ Bern Bern Switzerland Univ Calif Davis Davis CA 95616 USA

In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone rxs matrices. These algorithms can be used, for instance, to estimate a bimonotone regression function via least squares or (a smooth approximation of) least absolute deviations. Another application is shrinkage estimation in image denoising or, more generally, regression problems with two ordinal factors after representing the data in a suitable basis which is indexed by pairs (i,j)a{1,aEuro broken vertical bar,r}x{1,aEuro broken vertical bar,s}. Various numerical examples illustrate our methods.

关键词： active set algorithm Dynamic programming Estimated risk Pool-adjacent-violators algorithm Regularization

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Nonparametric Regression on a Graph

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2011年第2期20卷 432-447页

作者： Kovac, Arne Smith, Andrew D. A. C. Univ Bristol Dept Math Bristol BS8 1TW Avon England

The 'Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every vertex in the L-2 norm, and roughness is penalized on every edge in the L-1 norm. Thus the ideas of total variation penalization can be extended to a graph. The resulting minimization problem presents special computational challenges, so we describe a new and fast algorithm and demonstrate its use with examples. The examples include image analysis, a simulation applicable to discrete spatial variation, and classification. In our examples, penalized regression improves upon kernel smoothing in terms of identifying local extreme values on planar graphs. In all examples we use fully automatic procedures for setting the smoothing parameters. Supplemental materials are available online.

关键词： active set algorithm Image analysis Penalized regression Total variation

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The Bound-Constrained Conjugate Gradient Method for Non-negative Matrices

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2014年第3期162卷 931-953页

作者： Vollebregt, Edwin A. H. Delft Univ Technol DIAM NL-2600 GA Delft Netherlands VORtech BV NL-2600 AG Delft Netherlands

Existing conjugate gradient (CG)-based methods for convex quadratic programs with bound constraints require many iterations for solving elastic contact problems. These algorithms are too cautious in expanding the active set and are hampered by frequent restarting of the CG iteration. We propose a new algorithm called the Bound-Constrained Conjugate Gradient method (BCCG). It combines the CG method with an active-set strategy, which truncates variables crossing their bounds and continues (using the Polak-RibiSre formula) instead of restarting CG. We provide a case with n=3 that demonstrates that this method may fail on general cases, but we conjecture that it always works if the system matrix A is non-negative. Numerical results demonstrate the effectiveness of the method for large-scale elastic contact problems.

关键词： Quadratic program Bound constraints Conjugate gradients method active set algorithm Elastic contact problem

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