Waltraud Huyer

Address

Research Interests

• Global and local optimization
• Numerical analysis
• Data analysis
• Protein folding
• Population dynamics: structured populations

List of Publications

Publications in journals and refereed conference proceedings

1. W. Huyer, A size-structured population model with dispersion, J. Math. Anal. Appl. 181 (1994), 716-754
2. W. Huyer, Semigroup formulation and approximation of a linear age-dependent population problem with spatial diffusion, Semigroup Forum 49 (1994), 99-114
3. W. Huyer, On periodic cohort solutions of a size-structured population model, J. Math. Biol. 35 (1997), 908-934
dvi.gz file (47K), ps.gz file (129K)
We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable `substrate'. The model admits solutions with finitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter beta. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question whether n cohorts (n >= 2) with small size differences will tend to a periodic one-cohort solution as t tends to infinity.
4. W. Huyer, Well-posedness of a linear age-dependent population model with spatial diffusion in L^2, Advances in Mathematical Population Dynamics - Molecules, Cells and Man (O. Arino, D. Axelrod and M. Kimmel, eds.), World Scientific, Singapore, 1997, pp. 713-732
dvi.gz file (32K), ps.gz file (104K)
A linear model for an age-structured population with random diffusion in a bounded domain in R^n is studied in the framework in L^2. Three different approaches to establishing well-posedness of the problem are presented. Two of them involve applying known results on the m-dissipativeness of the sum of two m-dissipative operators to the population operator and the diffusion operator.
5. A. Neumaier, S. Dallwig, W. Huyer, and H. Schichl, New techniques for the construction of residue potentials for protein folding, Computational Molecular Dynamics: Challenges, Methods, Ideas (P. Deuflhard et al., eds.), Lecture Notes Comput. Sci. Eng. 4, Springer, Berlin, 1999, pp. 212-224
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A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the C(alpha) atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Ångström. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic programming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7Å of the PDB geometry, with one exception that has an error of 8.5Å.
6. W. Huyer and A. Neumaier, Global optimization by multilevel coordinate search, J. Global Optimization 14 (1999), 331-355
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Inspired by a method by Jones et al., we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an improved convergence result is obtained. We discuss implementation details and give some numerical results.
You can download a Matlab version of the algorithm here.
7. W. Huyer and A. Neumaier, A new exact penalty function, SIAM J. Optim. 13 (2003), 1141-1158
dvi.gz file (35K), ps.gz file (102K)
For constrained smooth or nonsmooth optimization problems, new continuously differentiable penalty functions are derived. They are proved exact in the sense that under some nondegeneracy assumption, local optimizers of a nonlinear program are precisely the optimizers of the associated penalty function. This is achieved by augmenting the dimension of the program by a variable that controls both the weight of the penalty terms and the regularization of the nonsmooth terms.
8. W. Huyer, Approximation of a linear age-dependent population model with spatial diffusion, Commun. Appl. Anal. 8 (2004), 87-108
ps.gz file (337K)
In this paper we first address the question under which conditions it is possible to obtain from Trotter-Kato approximations of two infinitesimal generators of C0-semigroups a Trotter-Kato approximation of the semigroup generated by the sum operator. This cannot be true in general since the sum operator might not even be a generator, and we derive sufficient conditions. However, when wellposedness is already established, it may be more convenient to verify the conditions of the Trotter-Kato theorem directly, taking into account the special structure of the problem. We consider the semigroup generated by an age-dependent population model with spatial diffusion, and numerical examples are presented to demonstrate feasibility of the scheme.
9. W. Huyer and A. Neumaier, Integral approximation of rays and verification of feasibility, Reliable Computing 10 (2004), 195-207
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An algorithm is presented that produces an integer vector nearly parallel to a given vector. The algorithm can be used to discover exact rational solutions of homogeneous or inhomogeneous linear systems of equations, given a sufficiently accurate approximate solution.
As an application, we show how to verify rigorously the feasibility of degenerate vertices of a linear program with integer coefficients, and how to recognize rigorously certain redundant linear constraints in a given system of linear equations and inequalities. This is a first step towards the handling of degeneracies and redundancies within rigorous global optimization codes.
10. A. Neumaier, O. Shcherbina, W. Huyer, and T. Vinko, A comparison of complete global optimization solvers, Math. Program., Ser. B 103 (2005), 335-356
Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables, collected from the literature. The test problems are available online in AMPL and were translated into the input formats of the various solvers using routines from the COCONUT environment. These translators are available online, too.
11. W. Huyer and A. Neumaier, SNOBFIT - stable noisy optimization by branch and fit, ACM Trans. Math. Software 35 (2008), No. 2, Article 9
ps.gz file (98K), pdf.gz file (225K)
The software package SNOBFIT for bound constrained noisy optimization of an expensive objective function is described. It combines global and local search by branching and local fits. The program is made robust and flexible for practical use by allowing for soft or hidden constraints, batch function evaluations, change of search regions, etc.
You can download a Matlab version of the algorithm here.
12. P. Pošík, W. Huyer, and L. Pál, A comparison of global search algorithms for continuous black-box optimization, Evolutionary Computation 20 (2012), 509-541
Four methods for global numerical black-box optimization with the origins in the mathematical programming community are described and experimentally compared with the state-of-the-art evolutionary method, BIPOP-CMA-ES. The methods chosen for the comparison exhibit various features potentially interesting for the evolutionary computation community: systematic sampling of the search space (DIRECT, MCS) possibly combined with a local search method (MCS), or a multistart approach (NEWUOA, GLOBAL) possibly equipped with a careful selection of points to run a local optimizer from (GLOBAL). The recently proposed "comparing continuous optimizers" (COCO) methodology was adopted as the basis for the comparison. Based on the results, we draw suggestions about which algorithm should be used depending on the available budget of function evaluations, and we propose several possibilities for hybridizing evolutionary algorithms with features of the other compared algorithms.
13. P. Pošík and W. Huyer, Restarted local search algorithms for continuous black-box optimization, Evolutionary Computation 20 (2012), 575-607
Several local search algorithms for real-valued domains (axis-parallel line search, Nelder-Mead simplex search, Rosenbrock's algorithm, quasi-Newton method, NEWUOA and VXQR) are described and thoroughly compared in this article, embedding them in a multistart method. Their comparison aims (1) to help the researchers from the evolutionary community to choose the right opponent for their algorithm (to choose an opponent that would constitute a hard-to-beat baseline algorithm), (2) to describe individual features of these algorithms and show how they influence the algorithm on different problems, and (3) to provide inspiration for the hybridization of evolutionary algorithms with these local optimizers. The recently proposed "comparing continuous optimizers" (COCO) methodology was adopted as the basis for the comparison. The results show that in low dimensional spaces, the old method of Nelder and Mead is still the most successful among those compared, while in spaces of higher dimensions it is better to choose an algorithm based on quadratic modeling, like NEWUOA or a quasi-Newton method.
14. W. Huyer and A. Neumaier, MINQ8: general definite and bound constrained indefinite quadratic programming, Comput. Optim. Appl. 69 (2018), 351-381
New algorithms for (i) the local optimization of bound constrained quadratic programs, (ii) the solution of general definite quadratic programs, and (iii) finding either a point satisfying given linear equations and inequalities or a certificate of infeasibility are proposed. The algorithms are implemented in Matlab and tested against state-of-the-art quadratic programming software.

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A. Neumaier, W. Huyer and E. Bornberg-Bauer, Hydrophobicity analysis of amino acids

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