Preprints

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Curriculum vita, including publications that are not available below:

1. Postscript file;
2. DVI file ;
3. PDF file
4. Send mail to rbk@louisiana.edu for further information.

Please cite properly any of this material that you use.

Papers

• A Review of Preconditioners for the Interval Gauss-Seidel Method, joint with Manuel Novoa and Chenyi Hu, Interval Computations 1 (1), pp. 59-85 (1991).

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• Numerical Tests of a Method for Simulating Electrical Potentials on the Cortical Surface, joint with R. D. Sidman, D. J. Major, and C. D. Hill, IEEE Trans. Biomed. Engrg. 38 (3), pp. 294-299 (1991).

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• Decomposition of Arithmetic Expressions to Improve the Behavior of Interval Iteration for Nonlinear Systems, preprint of an article that appeared in Computing 47 (2), pp. 169-191 (1991)

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• The Cluster Problem in Global Optimization: The Univariate case, joint with K. Du, preprint of an article that appeared in Computing (Suppl.) 9, pp. 117-127 (1992).

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• An Interval Branch and Bound Algorithm for Bound Constrained Optimization,Journal of Global Optimization 2, pp. 259-280 (1992).

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• Rigorous Computation of Surface Patch Intersection Curves, preprint (1993).

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• The Cluster Problem in Multivariate Global Optimization, joint with K. Du, preprint of an article that appeared in the Journal of Global Optimization 5, pp. 253-265 (1994).

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• An Interval Step Control for Continuation Methods, joint with Z. Xing, SIAM J. Numer. Anal. 31 (3), pp. 892-914 (1994).

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• INTLIB: A Portable FORTRAN 77 Elementary Function Library, ACM Trans. Math. Software 20 (4) pp. 447-459 (December, 1994).

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• A Fortran 90 Environment for Research and Prototyping of Enclosure Algorithms for Constrained and Unconstrained Nonlinear Equations, ACM Trans. Math. Software 21 (1), pp. 63-78 (March, 1995).

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• FORTDIFF: A Set of Subroutines for Fortran-to-Fortran Differentiation of Programs (technical report, 1995, joint with S. Ning)

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• A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems, in Applications of Interval Computations, ed. R. B. Kearfott and V. Kreinovich, Kluwer, Dordrecht, Netherlands, pp. 23-60, 1996.

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• Interval Computations: Introduction, Uses, and Resources, Euromath Bulletin 2 (1), pp. 95-112 (1996).

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Excerpt containing references to electronic resources (HTML)
• Automatic Differentiation of Conditional Branches in an Operator Overloading Context, in Computational Differentiation: Techniques, Applications, and Tools (proceedings of the Second International Workshop on Computational Differentiation), ed. M. Berz, C. Bischof, G. Corliss, and A. Griewank, SIAM, Philadelphia, pp. 75-81, 1996.

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• Interval Extensions of Non-Smooth Functions for Global Optimization and Nonlinear Systems Solvers, Computing 57 (2), pp. 149-162 (1996).

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Errata from Corliss and Van Iwaarden
• Treating Non-Smooth Functions as Smooth Functions in Global Optimization and Nonlinear Systems Solvers, preprint of an article that appeared in Scientific Computing and Validated Numerics, ed. G. Alefeld and A. Frommer, Akademie Verlag, pp. 160-172, 1996.

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• Test Results for an Interval Branch and Bound Algorithm for Equality-Constrained Optimization, preprint of an article that appeared in State of the Art in Global Optimization: Computational Methods and Applications, ed. C. Floudas and P. Pardalos, Kluwer, Dordrecht, pp. 181--200, 1996.

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• Optimal Preconditioners for Interval Gauss-Seidel Methods, joint with S. Shi, in Scientific Computing and Validated Numerics, ed. G. Alefeld and A. Frommer, Akademie Verlag, pp. 173-178, 1996.

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• A Comparison of some Methods for Solving Linear Interval Equations, joint with S. Ning, SIAM J. Numer. Anal. 34 (1), pp. 1289-1305 (August, 1997)

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• Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 Module for an Interval Data Type, preprint of a paper that appeared in ACM Trans. Math. Software 22 (4), pp. 385-392 (1996).

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• Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Algebraic Systems, in the SIAM Journal on Scientific Computing, 18 (2), pp. 574-594 (March, 1997).

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• On Proving Existence of Feasible Points in Equality Constrained Optimization Problems,  Mathematical Programming 83 (1), pp. 89-100 (September, 1998).

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• On Verifying Feasibility in Equality Constrained Optimization Problems (technical report to supplement the above).

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• An Iterative Method for Finding Approximate Feasible Points, (joint with J. Dian), technical report.

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• Rigorous Global Search: Industrial Applications, (joint with G. F. Corliss), in Developments in Reliable Computing, ed. T. Csendes, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 1-16, 1999.

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On Stopping Criteria in Verified Nonlinear Systems or Optimization Algorithms  (preprint of the article  R. B. Kearfott and G. W. Walster, "On Stopping Criteria in Verified Nonlinear Systems or Optimization Algorithms," ACM Trans. Math. Software26 (3), pp. 323-351 (September, 2000))
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• Existence Verification for Singular Zeros of Nonlinear Systems, (joint with J. Dian and A. Neumaier), technical report (expanded explanations of parts the article  R. Baker Kearfott, Jianwei Dian, and A. Neumaier, “Existence Verification for Singular Zeros of Complex Nonlinear Systems,” SIAM J. Numer. Anal. 38 (2), pp. 360--379 (2000). )

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• Taylor Series Models in Deterministic Global Optimization (joint with A. Arazyan), accepted for publication in the proceedings of AD 2000, the Third International Conference and Workshop on Automatic Differentiation, June 19-23, 2000, Nice, France (to be published by SIAM)

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• An Example of Singularity in Global Optimization, accepted for publication in  Reliable Computing.

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• Verifying Topological Indices for Higher-Order Rank Deficiencies, submitted for the proceedings of the 2000 AMS-IMS-SIAM summer research conference on Algorithms and their Complexity for Nonlinear Problems, July 16 to July 20, 2000, Mt. Holyoke College, edited by Christopher Sikorski.

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• Existence Verification for Higher Degree Singular Zeros of

Complex Nonlinear Systems, joint with Jianwei Dian, submitted to the SIAM Journal on Numerical Analysis.
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• Encyclopedia of Optimization articles:
• Interval Newton Methods: Postscript file; DVI file; PDF file
• Interval Fixed Point Theory: Postscript file; DVI file; PDF file
• Verifying Feasibility: Postscript file; DVI file; PDF file
• Unconstrained and Constrained Optimization: Postscript file; DVI file; PDF file
• Nondifferentiable Problems: Postscript file; DVI file; PDF file
• Intermediate Terms: Postscript file; DVI file; PDF file

 

Talks

• A Series of Related Talks on GlobSol
• A Brief Introduction to Global Optimization and a Preview of INTOPT_90, talk given to the Department of Mathematics, Statistics, and Computer Science, Marquette University, October 16, 1997.

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• GlobSol, A Fortran 90 Package for Rigorous Global Search, talk given at the 1997 International Symposium on Mathematical Programming, Lausanne, Switzerland, August 25-29, 1997.

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• The GlobSol Software: An Overview and Examples, presented at the 1998 SIAM Annual Meeting, Toronto, Canada, July 16, 1998.

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• The GlobSol Project: Rigorous Global Solutions (Overview and Recent Developments), minisymposium presentation at the 1999 joint SIAM Annual Meeting and Optimization Conference, Atlanta, Georgia, USA, May 11, 1999.

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• Rigorous Global Optimization and the GlobSol Package, colloquium lecture given to the mathematical sciences department at the University of Houston-Downtown, September 23, 1999.

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• An Overview of the GlobSol Package, talk given at the Fall, 1999 INFORMS meeting, Philadelphia, Pennsylvania, November 7, 1999.

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• An Overview of the GlobSol Package for Verified Global Optimization, talk given at the Institute of Scientific Computing, Technical University of Dresden, July, 2000.

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• Computational Differentiation in Global Optimization Software, talk given at a minisymposium on the interaction on interval analysis and computational differentiation, SIAM National Meeting, Stanford, California, July 14-18, 1997

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• Automatic Verification of Dynamical System Properties, presented at an Institute of Mathematics and its Applications workshop on the Dynamics of Algorithms, University of Minnesota, Minneapolis, November 17--21, 1997.

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• Verified Linear and Nonlinear Systems Computations -- Techniques and Practicalities, presented at the 1998 SIAM Annual Meeting, Toronto, Canada, July 16, 1998.

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• Existence and Uniqueness Verification for Singular Zeros of Nonlinear Systems, presented SCAN'98 (Validated Numerics and Scientific Computation), Budapest, Hungary, September 22-25, 1998.

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• Existence Verification for Singular Zeros of Nonlinear Systems, presented by Jianwei Dian, minisymposium presentation at the 1999 joint SIAM Annual Meeting and Optimization Conference, Atlanta, Georgia, USA, May 13, 1999.

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• Efficient Verification of the Topological Index of Real Solutions to Algebraic Systems, joint with Jianwei Dian, presented at the 2000 Southeastern Section Meeting of the American Mathematical Society (Meeting #954), April 14-16, 2000, Lafayette, Louisiana. A variant of this talk was also given at the 2000 AMS-IMS-SIAM summer research conference on Algorithms and their Complexity for Nonlinear Problems, July 16 to July 20, 2000, Mt. Holyoke College, organized by Eugene Allgower, Kurt Georg, and Christopher Sikorski.

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• Multivariate Taylor Models in Global Optimization, talk given at AD 2000,  the third International Conference/Workshop on Automatic Differentiation: From Simulation to Optimization, June 19-23, 2000, Nice, France.  (Variants were also given at an informal workshop on Taylor models in automatic differentiation hosted by Martin Berz at the National Superconducting Cyclotron Laboratory, Michigan State University, February 17-20, 2000 and as a colloquium lecture at the University of Louisiana at Lafayette, March 16, 2000)

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• of Numerical Toolbox for Verified Computing I, by R. Hammer, M. Hocks, U. Kulisch and D. Ratz, for Zentralblatt f. Mathematik.

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• of Numerica: A modeling Language for Global Optimization, by P. van Hentenryck, L. Michel, and Y. DeVille, for the Mathematics of Computation.

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• of Computational Complexity and Feasibility of Data Processing and Interval Computations, by V. Kreinovich, A. Lakeyev, J. Rohn, and P. Kahl, for Reliable Computing.

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• National Science Foundation Grant CCR-9203730
• National Science Foundation Grant DMS-9701540
• SunSoft Cooperative Research Grant:  The GlobSol  project