Search results for "MathematicsofComputing_NUMERICALANALYSIS"
showing 10 items of 149 documents
A variational inequality approach to constrained control problems for parabolic equations
1988
A distributed optimal control problem for parabolic systems with constraints in state is considered. The problem is transformed to control problem without constraints but for systems governed by parabolic variational inequalities. The new formulation presented enables the efficient use of a standard gradient method for numerically solving the problem in question. Comparison with a standard penalty method as well as numerical examples are given.
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
How to simulate normal data sets with the desired correlation structure
2010
The Cholesky decomposition is a widely used method to draw samples from multivariate normal distribution with non-singular covariance matrices. In this work we introduce a simple method by using singular value decomposition (SVD) to simulate multivariate normal data even if the covariance matrix is singular, which is often the case in chemometric problems. The covariance matrix can be specified by the user or can be generated by specifying a subset of the eigenvalues. The latter can be an advantage for simulating data sets with a particular latent structure. This can be useful for testing the performance of chemometric methods with data sets matching the theoretical conditions for their app…
AMaLGaM IDEAs in noiseless black-box optimization benchmarking
2009
This paper describes the application of a Gaussian Estimation-of-Distribution (EDA) for real-valued optimization to the noiseless part of a benchmark introduced in 2009 called BBOB (Black-Box Optimization Benchmarking). Specifically, the EDA considered here is the recently introduced parameter-free version of the Adapted Maximum-Likelihood Gaussian Model Iterated Density-Estimation Evolutionary Algorithm (AMaLGaM-IDEA). Also the version with incremental model building (iAMaLGaM-IDEA) is considered.
A fast 3D dual boundary element method based on hierarchical matrices
2008
AbstractIn this paper a fast solver for three-dimensional BEM and DBEM is developed. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. Special algorithms are developed to deal with crack problems within the context of DBEM. The structure of DBEM matrices has been efficiently exploited and it has been demonstrated that, since the cracks form only small parts of the whole structure, the use of hierarchical matrices can be particula…
COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS
2005
We propose a new method to calibrate the local volatility function of an asset from observed option prices of the underlying. Our method is initialized with a preprocessing step in which the given data are smoothened using cubic splines before they are differentiated numerically. In a second step the Dupire equation is rewritten as a linear equation for a rational expression of the local volatility. This equation is solved with Tikhonov regularization, using some discrete gradient approximation as penalty term. We show that this procedure yields local volatilities which appear to be qualitatively correct.
Error bounds for a convexity-preserving interpolation and its limit function
2008
AbstractError bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.
Memetic Algorithms in Engineering and Design
2012
When dealing with real-world applications, one often faces non-linear and nondifferentiable optimization problems which do not allow the employment of exact methods. In addition, as highlighted in [104], popular local search methods (e.g. Hooke-Jeeves, Nelder Mead and Rosenbrock) can be ill-suited when the real-world problem is characterized by a complex and highly multi-modal fitness landscape since they tend to converge to local optima. In these situations, population based meta-heuristics can be a reasonable choice, since they have a good potential in detecting high quality solutions. For these reasons, meta-heuristics, such as Genetic Algorithms (GAs), Evolution Strategy (ES), Particle …
A Projected Algebraic Multigrid Method for Linear Complementarity Problems
2011
We present an algebraic version of an iterative multigrid method for obstacle problems, called projected algebraic multigrid (PAMG) here. We show that classical AMG algorithms can easily be extended to deal with this kind of problem. This paves the way for efficient multigrid solution of obstacle problems with partial differential equations arising, for example, in financial engineering.
Decision Making on Pareto Front Approximations with Inherent Nondominance
2011
t Approximating the Pareto fronts of nonlinear multiobjective optimization problems is considered and a property called inherent nondominance is proposed for such approximations. It is shown that an approximation having the above property can be explored by interactively solving a multiobjective optimization problem related to it. This exploration can be performed with available interactive multiobjective optimization methods. The ideas presented are especially useful in solving computationally expensive multiobjective optimization problems with costly function value evaluations. peerReviewed