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2. The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems.
- Author
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Birgin, ErnestoG., Fernández, Damián, and Martínez, J.M.
- Subjects
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NONLINEAR programming , *NUMERICAL analysis , *LAGRANGE equations , *APPROXIMATION theory , *PROBLEM solving , *MATHEMATICAL proofs , *ALGORITHMS - Abstract
Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
3. A hybrid algorithm for approximate optimal control of nonlinear Fredholm integral equations.
- Author
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Borzabadi, AkbarH., Fard, OmidS., and Mehne, HamedH.
- Subjects
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ALGORITHMS , *FREDHOLM equations , *NONLINEAR theories , *ITERATIVE methods (Mathematics) , *STOCHASTIC convergence , *NUMERICAL analysis , *APPROXIMATION theory - Abstract
In this paper, a novel hybrid method based on two approaches, evolutionary algorithms and an iterative scheme, for obtaining the approximate solution of optimal control governed by nonlinear Fredholm integral equations is presented. By converting the problem to a discretized form, it is considered as a quasi-assignment problem and then an iterative method is applied to find an approximate solution for the discretized form of the integral equation. An analysis for convergence of the proposed iterative method and its implementation for numerical examples are also given. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
4. Rational algorithm for quadratic Christoffel modification and applications to the constrained L -approximation.
- Author
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Cvetković, A.S., Milovanović, G.V., and Matejić, M.M.
- Subjects
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ALGORITHMS , *QUADRATIC equations , *CHEBYSHEV polynomials , *ORTHOGONAL polynomials , *CHRISTOFFEL-Darboux formula , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, , where it is allowed z to be in supp(d σ). Also, we present an application of modified algorithm to the measures and , where T 2(t)=t 2−½ is the second degree monic Chebyshev polynomial of the first kind and , , is the Chebyshev measure of the second kind. Also, we present an application to the constrained L 2-polynomial approximation. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
5. A symmetric rank-one quasi-Newton line-search method using negative curvature directions.
- Author
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Öztoprak, Figen and Birbil, Ş.İlker
- Subjects
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MATHEMATICAL symmetry , *ITERATIVE methods (Mathematics) , *MATHEMATICAL optimization , *APPROXIMATION theory , *NUMERICAL analysis , *STOCHASTIC convergence , *ALGORITHMS - Abstract
We propose a quasi-Newton line-search method that uses negative curvature directions for solving unconstrained optimization problems. In this method, the symmetric rank-one (SR1) rule is used to update the Hessian approximation. The SR1 update rule is known to have a good numerical performance; however, it does not guarantee positive definiteness of the updated matrix. We first discuss the details of the proposed algorithm and then concentrate on its practical behaviour. Our extensive computational study shows the potential of the proposed method from different angles, such as its performance compared with some other existing packages, the profile of its computations, and its large-scale adaptation. We then conclude the paper with the convergence analysis of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
6. A New Method for Deriving Waiting-Time Approximations in Polling Systems with Renewal Arrivals.
- Author
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Dorsman, J.L., van der Mei, R.D., and Winands, E. M. M.
- Subjects
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QUEUING theory , *APPROXIMATION theory , *ALGORITHMS , *NUMERICAL analysis , *COMPUTER simulation , *DATA transmission systems simulations , *PARAMETER estimation - Abstract
We study the waiting-time distributions in cyclic polling models with renewal arrivals, general service and switch-over times, and exhaustive service at each of the queues. The assumption of renewal arrivals prohibits an exact analysis and reduces the available analytic results to heavy-traffic asymptotics, limiting results for large switch-over times and large numbers of queues, and some numerical algorithms. Motivated by this, the goal of this paper is to propose a new method for deriving simple closed-form approximations for the complete waiting-time distributions that work well for arbitrary load values. Extensive simulation results show that the approximations are highly accurate over a wide range of parameter settings. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
7. Estimation of daily-integrated PAR from sparse satellite observations: comparison of temporal scaling methods.
- Author
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Wang, Dongdong, Liang, Shunlin, Liu, Ronggao, and Zheng, Tao
- Subjects
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SPECTRORADIOMETER , *ALGORITHMS , *NUMERICAL analysis , *INTERPOLATION , *APPROXIMATION theory , *SPECTROPHOTOMETERS , *SPECTROMETERS , *RADIOMETERS , *SPECTROSCOPE , *ABSORPTIOMETER - Abstract
Incident Photosynthetically Active Radiation (PAR) is a critical parameter for modelling ecosystem productivity. An algorithm for estimating instantaneous PAR from Moderate Resolution Imaging Spectroradiometer (MODIS) data was developed earlier; however, daily-integrated PAR is more meaningful than instantaneous PAR in many cases because many land surface models require a daily or coarser temporal resolution. This paper compares two different algorithms (adjusted sinusoidal interpolation and look-up table) for estimating daily-integrated PAR from instantaneous PAR values. Statistical analysis of the validation results indicates that the look-up table method more accurately estimates daily-integrated PAR than the use of adjusted sinusoidal interpolation. We also investigated how window size, daytime length and the number of overpass counts per day affect bias and the relative error of estimation. Validation using field measurements, and comparison with the Geostationary Operational Environmental Satellites PAR product, demonstrates that data collected by MODIS can be used to provide reliable estimates of daily-integrated PAR. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
8. An evaluation of void-filling interpolation methods for SRTM data.
- Author
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Reuter, H. I., Nelson, A., and Jarvis, A.
- Subjects
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ALGORITHMS , *ALTITUDES , *GEOLOGICAL statistics , *RADAR , *INTERPOLATION , *NUMERICAL analysis , *APPROXIMATION theory , *RELIEF models , *ELECTRONIC systems - Abstract
The Digital Elevation Model that has been derived from the February 2000 Shuttle Radar Topography Mission (SRTM) has been one of the most important publicly available new spatial data sets in recent years. However, the 'finished' grade version of the data (also referred to as Version 2) still contains data voids (some 836,000 km2) - and other anomalies - that prevent immediate use in many applications. These voids can be filled using a range of interpolation algorithms in conjunction with other sources of elevation data, but there is little guidance on the most appropriate void-filling method. This paper describes: (i) a method to fill voids using a variety of interpolators, (ii) a method to determine the most appropriate void-filling algorithms using a classification of the voids based on their size and a typology of their surrounding terrain; and (iii) the classification of the most appropriate algorithm for each of the 3,339,913 voids in the SRTM data. Based on a sample of 1304 artificial but realistic voids across six terrain types and eight void size classes, we found that the choice of void-filling algorithm is dependent on both the size and terrain type of the void. Contrary to some previous findings, the best methods can be generalised as: kriging or inverse distance weighting interpolation for small and medium size voids in relatively flat low-lying areas; spline interpolation for small and medium-sized voids in high-altitude and dissected terrain; triangular irregular network or inverse distance weighting interpolation for large voids in very flat areas, and an advanced spline method (ANUDEM) for large voids in other terrains. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
9. State-Constrained Optimal Control for the Phase-Field Transition System.
- Author
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Moroşanu, C. and Wang, G.
- Subjects
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FINITE element method , *NUMERICAL analysis , *NUMERICAL solutions to equations , *APPROXIMATION theory , *ALGORITHMS - Abstract
This paper deals with the existence and necessary optimality conditions for an optimal control problem governed by a phase-field transition system. The one-point boundary (time variable) state condition is considered. A numerical algorithm of gradient type and numerical implementation are reported, too. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
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