VITAE - Weldon A. Lodwick
Institution Date Degree Major
Thesis title: "Two Numerical Methods for the
Solution of Optimal Control Problems With Computed Error Bounds Using the
Maximum Principle of Pontryagin"
Supervisor: Dr. Joel Davis
PROFESSIONAL EXPERIENCE (last 25 years)
2003 – present Full
Professor of Mathematics,
1989 – 2003 Associate
Professor of Mathematics,
1982 - 1989 Assistant
Professor of Mathematics,
1991 - 1993 Visiting
Associate Professor, Systems Analysis, Miami University, Oxford, Ohio
1977 - 1982 Research Assistant and Assistant Professor, Department of Resource Development and co-director of the MSU/CRIES international project in Central America, Caribbean, and Syria, Michigan State University and Organization of American States
AWARDS
and OFFICES
2004 – Editorial Board Fuzzy Sets and
Systems and President of the
Special Interest Group in Optimization of IFSA (International Fuzzy System
Association)
2000 – Fulbright Research Fellowship
1994-1995 Outstanding Faculty
– granted by students of the
1972 – Star Teacher,
PUBLICATIONS -
refereed
2004
Fonte, Cidalia and Lodwick, Weldon A.,
“Areas of Fuzzy Geographical Entities.” International Journal of Geographical
Information Systems, Volume 18 No. 2, March 2004, pp. 127-150.
2003
Fonte, Cidalia and Lodwick, W.,
“Modeling the fuzzy spatial extent of geographical entities” in Cobb, M., Petry, F., and Robinson, V. (editors), Fuzzy Modeling with Spatial Information for
Geographical Problems, Springer-Verlag, (late
2003).
Lodwick, W.A. and Jamison, K.D., "Estimating
and Validating the Cumulative Distribution of a Function of Random Variables:
Toward the Development of Distribution Arithmetic," Reliable Computing,
Vol. 9, No. 2, April 2003, pp. 127-141.
Lodwick,
W.A. and
2002
Jamison, K.D., and
Lodwick, W.A., “The Construction of Consistent Possibility and Necessity
Measures,” Fuzzy Sets and Systems
Vol. 132:1, November 2002, pp. 1-10.
Russell, S., and Lodwick, W.A., “Fuzzy Game Theory and Internet Commerce:
e-Strategy and Metarationality,” NAFIPS’2002
– Proceedings, June, 2002.
2001
Lodwick, W.A.,
Neumaier, A. and Newman, F. D., “Optimization
Under Uncertainty: Methods and Applications in Radiation Therapy,” Proceedings 10th IEEE International Conference on Fuzzy
Systems 2001, Volume 3, pp.
1219-1222.
Lodwick, W.A., Jamison, K. D. and Newman, F.
D., “Extension of Interval Validation Methods to Fuzzy Set Theory,” NAFIPS’2001 – Proceedings,
edited by Larry Hall, July, 2001, pp. 1665-1670.
Jamison, K. D., Lodwick, W.A. and Newman, F.
D., “Optimization Under Uncertainty Using Possibility
and Necessity Distributions Consistent with Probability Distributions,” NAFIPS’2001-Proceedings, edited by Larry Hall, July, 2001, pp.
1671-1676.
Jamison, K.D. and Lodwick, W.A., "Fuzzy Linear Programming Using Penalty Method," Fuzzy Sets and Systems, Vol. 119, 2001, pp. 97-110.
2000
Lodwick, W.A. and.Jamison, K.D. and Russell, D.,
“A Comparison of Fuzzy, Stochastic and Deterministic Methods in Linear
Programming,” 19th International Conference of
the North American Fuzzy Information Processing Society, edited by Thomas Whalen, July 2000, pp.
321-325.
1999
Lodwick, W.A. and Russell, D., “The Use of Fuzzy Optimization Methods for Radiation Therapy of Tumors,” 18th International Conference of the North American Fuzzy Information Processing Society, edited by Rajesh N. Dave and Thomas Sudkamp, June 1999, pp.288-293.
Russell, D. and Lodwick, W.A., "Fuzzy Clustering in Data Mining for Telco Database Marketing Campaigns," 18th International Conference of the North American Fuzzy Information Processing Society, edited by Rajesh N. Dave and Thomas Sudkamp, June 1999, pp. 720-726.
Jamison, K.D. and Lodwick, W.A., "Minimizing
Unconstrained Fuzzy Functions," Fuzzy Sets and Systems, Vol.
103,No. 3, May 1999, pp. 457-467.
1998
Lodwick, W.A. and Jamison, K.D. " Fuzzy Optimization: Computational
Methods and Applications to Radiation Therapy of Tumors," EUFIT ’98
Vol. 3, Verlag
Lodwick, W.A., S.
McCourt, D. Newman, and S. Humphries, “Optimization Methods for Radiation
Therapy Plans,” in Borgers, Christof and Natterer, Frank (editors) IMA
Series in Applied Mathematics - Computational Radiology and Imaging: Therapy
and Diagnosis, Springer-Verlag, 1998.
1997
Lodwick W.A. and Jamison, K.D., “A
Computational Method for Fuzzy Optimization,” in Ayyub, Bilal and Gupta, Madan
(editors), Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic,
Statistics, and Neural Network Approach, Kluwer Academic Publishers, 1997.
Lodwick, W.A., and
Jamison, K.D., "Interval Methods and Fuzzy Optimization," International
Journal of Uncertainty, Fuzziness and Knowledge-Based Reasoning, Vol. 5, No.
3, June, 1997, pp. 239-250.
1996
Corliss, G. and Lodwick, W.A.,
"Correct Computation of Solutions of Differential Algebraic Control
Equations," Zeitsschrift fuer Angewandte Mathematik und Machanik (ZAMM)
Special Volume: Numerical, Scientific Computing, Computer Science, 1996,
Akademie Verlag,
1992
Lodwick, W.A. and Levine, R., Chapter
3: "Sensitivity of Parameter and Loop Structures," pp. 43-86, Chapter
4: "Psychological Scaling and Filtering of Errors in Empirical
Systems," pp. 87-118, Chapter 5: "Parameter Estimation and Assessing
the Fit of Dynamic Models," pp. 119-150, in Analysis of Dynamic
Psychological Systems: Methods and Applications, Volume 2, edited by, Ralph
Levine and Hiram Fitzgerald, Plenum Press, 1992
Lodwick, W.A.
"Preprocessing Nonlinear Functional Constraints with Application to the
Pooling Problem," ORSA Journal on Computing, Vol. 4 No. 2, May,
1992, pp. 119-131.
1990
Lodwick, W.A., "A Generalized
Convex Stochastic Dominance Algorithm," IMA Journal of Mathematics in
Business and Industry, Vol. 2, No.3, Nov. 1990, pp. 225-246.
Lodwick, W., A.
"Analysis of Structure in Fuzzy Linear Programs," Fuzzy Sets and
Systems, Vol. 38, No. 1, October 1990, pp. 15-26.
Lodwick, W.A., W.
Munson, and L. Svoboda, "Attribute Error and Sensitivity Analysis of Map
Operations in Geographic Information Systems: Suitability Analysis" The
International Journal of Geographic Information Systems, Vol. 4, No. 4,
October 1990, pp. 413-428.
1989
Lodwick, W.A., "Constraint
Propagation, Relational Arithmetic in AI Systems and Mathematical
Programs," Annals of OR, Special Issue: Linkages with Artificial
Intelligence, Vol. 21 (1989), pp. 143-148.
Lodwick, W.A.,
"Developing Confidence Limits on Errors of Suitability Analyses in
Geographic Information Systems," in Goodchild, M. and Suchi, G. (eds), Accuracy
of Spatial Databases, Taylor and D., London, United Kingdom, 1989, pp.
69-78.
1988
Lodwick, W.A., "The Use of
Interval Analysis to Uncover Structures of Linear Systems," in Moore, R.E.
(ed), Proceedings of the International Workshop on Reliability and Computing,
Academic Press, 1988, pp. 341-353.
Lodwick, W.A.,
"Fuzzy Set Theoretic Approaches to Natural Language in Decision Support
Systems," in Mitra, G. (ed), Proceedings of the NATO ASI Conference on
Mathematical Models for Decision Support, Springer Verlag, 1988, pp.
575-584.
1984
Robison, L., Cochran, M. and Lodwick,
W.A., "Improving the Efficiency of Stochastic Dominance Techniques using
Convex Set Stochastic Dominance," American Journal of Agricultural
Economics Vol. 67, No. 2, 1984, pp. 289-295.
Jamison, K. D. and Lodwick, W.A., “Interval-Valued Probability Measures,”
UCD/CCM Report No. 213, July, 2004 (submitted for publication)
Lodwick, W.A. and Bachman, K.A. ,
“Solving Large-Scale Fuzzy and Possibiliistic
Optimization Problems: Theory, Algorithms and Applications,” UCD/CCM Report No.
212, June, 2004 (submitted for publication)
Jamison, K. D., Lodwick, W.A., and Olsen, G.., “A Method for Finding an
Optimal Investment Strategy for an Individual Retiree,” UCD/CCM Report No. 204,
October, 2003 (submitted for publication)
Jamison, K. D.,
Lodwick, W.A., and Kawai, M., “A Simple Closed Form estimate of the Cumulative
Distribution Function a Monotone Function of a Random Variable,” UCD/CCM Report
No. 187, May, 2002.
Fonte, C., and
Lodwick, W.A., “Modeling and Processing the Positional Uncertainty of
Geographical Entities with Fuzzy Sets,” UCD/CCM Report No. 176, August, 2001.
Corliss, G. and
Lodwick, W.A., "The Role of Constraints in the Validated Solution of
DAEs,"
Lodwick, W.A.
“Constrained Interval Arithmetic,” UCD/CCM Report No. 138, February, 1999.
Lodwick, W.A.
“Computing Minimal Admissible Sets in Decision Making Under Risk Using Convex
Stochastic Dominance – Parts 1/2,” UCD/RP 86-0101 and 86-0102, January 1986.
Lodwick, W.A. “A New
Stochastic Dominance Criterion,” UCD/RP 85-1201, December 1985.
Lodwick, W.A. “Interval
Analysis and Optimal Control: Automatic Computation of Errors for Constrained
and Unconstrained Problems,” UCD/RP 85-1002, October, 1985.
Lodwick, W.A., “Two Interval
Analytic Methods for Solving Unconstrained Optimal Control Problems Using Integral
Equations with Automatically Computed Error Bounds,” UCD/RP 85-1001, October
1985.
TALKS (selected)
2004
INFORMS’04,
NAFIPS’04,
2003
Federal
University of Rio Grande do Sul Department of Mathematics, Porto Alegre, Rio
Grande do Sul, “Mathematical Models in Radiation Therapy,” July 3, 2003.
Brazilian Space Agency (INPE) – Applied Mathematics Group, São Jose dos Campos, São Paulo,
Brazil, “Uncertainty Surface Mapping” and “Optimization Under Uncertain,” May
30, 2003.
University of Campinas, Department
of Applied Mathematics and Department of Electrical Engineering, Campinas, São Paulo, Brazil,
“Workshop on Optimization Models Under Uncertainty With Applications to
Radiation Therapy of Tumors,” May 26-31, 2003.
2002
Highlighted Talk, 2002
2001
10th IEEE Conference on Fuzzy Systems, Invited Speaker
(Optimization and Decision Making) “Consistent Possibilistic Optimization in
Radiation Therapy Problems,” December, 2001,
NAFIPS’2001, “The Extension of Interval Validation
Methods to Fuzzy Set Theory,” July 2001,
2000
Ruhr-University
Katholieke
Universiteit Nijmegen (Netherlands), Informal talk to graduate students and
professor of the Department Computer Science, “Interval Analysis Methods and
Complexity Reduction in Proof Assistants (Computerized Proofs),” November 8,
2000.
NAFIPS’2000,
“A Comparison of Fuzzy, Stochastic and Deterministic Methods in Linear
Programming,” July 2000,
1999
NAFIPS’1999, “The Use of Fuzzy
Optimization Methods for Radiation Therapy of Tumors,”,
1998
SIAM Annual Meeting – Minisymposium on
Validated Solutions of Ordinary Differential Equations and Differential
Algebraic Equations, “The Role of Constraints in Computing Validated Solutions
to Differential Algebraic Equations.”
1997
Institute for Mathematics and its
Applications Conference on Computational Radiology and Imaging: Therapy and
Diagnosis (invited speaker) –
1996
George Corliss
(Marquette University) presenter, “The Role of Constraints in the Validated
Solution of DAE’s”, International Conference on Interval Methods and Computer
Aided Proofs in Science and Engineering, Wurtzburg, Germany.
1995
Arnold Neumaier (
ICIAM Hamburg 95,
“Correct Computation of Solutions of Differential Algebraic Control Equations,”
George Corliss presenter.
ISUMA-NAFIPS’95 (North American Information
Processing Society) The 3rd International Symposium on Uncertainty Modeling and
Analysis, Invited Talk, “Fuzzy and Interval Nonlinear Optimization: Theory and
Computational Methods,”
1993
Conference on Numerical Result
Verification, University of Southwest Louisiana, Lafayette, Louisiana (one talk
and chaired one session), February 25 - March 1, 1993
1992
(By Invitation Only - German Government
with NSF Travel grant) Schloss DagStuhl Internationales Begegnungsund
Forschungszentrum fur Informatik Conference on Symbolic, Algebraic and
Validated Numerical Computation Algebra, "Three Applications of Interval
Methods for Computing Feasible Regions of Nonlinear Systems," Schloss
DagStuhl, W-6648 Wadern, Germany, August 3-7, 1992
1991
Invited speaker at the 11th Roundtable
for the development of an Intelligent Mathematical Programming System, November
,1991
1990
Invited Speaker at the ORSA/TIMS Spring
meeting to a special session of Operations Research Applied to the Petroleum
Industry (May 1990, Las Vegas, Nevada).
“Error Propagation
and Sensitivity Analysis in Geographical Information Systems,”
1989
Intelligent Mathematical Programming
Roundtable #6 – “Extensions of LP Reductions for the (Nonlinear) Pooling
Problem,”
1988
”Confidence Limits in Geographic
Analysis - Suitability Analysis,” Specialist Meeting on Accuracy in Spatial
Databases,
“Finding
Redundancies and Reduction in Fuzzy Linear Programming Problems,” The 13th
International Symposium on Mathematical Programming, August 29-September 2,
1988, Tokyo, Japan (presented by H. Greenberg).
“Finding
Redundancies and Infeasibilities in Linear Programs with Bounded Perturbed
Coefficients,” 10th Symposium on Mathematical Programming with Data
Perturbation, 26-27 May, 1988, The George Washington University, Washington,
DC.
1987
”Fuzzy Set Theoretical Approaches to
Natural Language Processing in Decision Support Systems,” NATO Advanced Study
Institute, Val d'Isere, France, August, 1987.
”The CU-Denver
Mathematics Clinic,”
2003 NAFIPS’03,
co-organizer of special session on interval analysis
2002 – Organizing Committee, Scientific
Committee, organizer of panels, and referee for a three-day symposium: 2002
SIAM Workshop on Validated Computing. I
had the initial idea and the gathering of the group of people that make up the
organizing committee.
Editor for the
Special Issue for Reliable Computing
on Linkages Between Interval Mathematics and Fuzzy Set Theory.
INFORM Workshop –
NAFIPS’02, co-organizer of special session on interval
analysis
2001 – Editor for the Special Issue of Fuzzy Sets
and Systems on the Interfaces Between Fuzzy Set Theory and Interval
Analysis.
2000 – International Committee and Special
Session Organizer (Fuzzy Optimization) for NAFIPS’2000.
Referee: I average 8-10 manuscripts per year
RELATED ACTIVITIES
1967-1969: I
began a mathematics tutoring for at-risk African American high school students
in
1969-1973: I obtained my teaching certificate, taught 8th -12th
grade mathematics including advanced placement and remedial mathematics
courses, rural
1969-1973: I was actively involved with the local NEA becoming the first
white president (under a ten year racial rotation) of the desegregated
association for
Burke
for
the county.
1973: Upward Bound Teacher,
1973-1977: Involved with a volunteer program at the Federal
Penitentiary,
of
these courses.
1977-1982: I worked in
of resource trade-off issues). I also worked with Syrian officials to transfer computerized systems for agricultural census (statistical systems).
1987-1988: I
was “on loan” (EPA Grant) to EPA Region 8 as a resident mathematician and help
develop region 8’s geographical information system and analysis laboratory.
OTHER: I speak Portuguese and Spanish fluently.
MATHEMATICS CLINICS TAUGHT
Watson & Wyatt - Mathematical Models for Risk Analysis of Portfolio Investments (Spring
2003) UCHSC Department of Radiation Oncology- Medical Image Processing
and Radiation Therapy of Tumors (Fall semester, 2002)
Computerized
Medical Systems (Saint Louis, Missouri) - Radiation Therapy of
Cancer Tumors (two semesters)
United States Department of Agriculture, Plant Variety Protection Office
(Beltsville, Maryland) - Intelligent System for Plant Protection Applications
(one semester) semesters
Martin Marietta Company - Dynamical Systems and Neural Networks (two
semesters)
Water Models – un-sponsored (one
semester)
Central Bank of Denver - Portfolio Models (one semester)
SERVICE
Director and Secretary (1997-2006),
an elected position – South Englewood Sanitation District 1