Earl R. Barnes

Born: 1942

Birthplace: South Carolina

B.S. in (1964) in Mathematics Morgan State University

Ph.D. in Mathematics from the University of Maryland in 1968
thesis: The Optimal Control of Systems with Distributed Parameters; advisor: G. S. Jones

Area of Research Interests: linear and nonlinear programming techniques, and graph theory

: Professor of School of Industrial and Systems Engineering of Georgia Institute of Technology

URL: http://www.isye.gatech.edu/people/faculty/Earl_Barnes/
email: ebarnes@isye.gatech.edu

Earl R. Barnes earned his B.S. in Mathematics from Morgan State University in 1964. He was part of the famous Morgan State class which inventually produced four with a doctrate. He earned his Ph.D. in Mathematics from the University of Maryland in 1968. From 1968-1988 Dr. Barnes worked for International Business Machines (IBM) at their Research Center in Yorktown heights, N.Y. During that time he also held several acedemic appointments, including one year appointments at the University of Wisconsin, Madison, and M.I.T., and a nine year adjunct appointment in Industrial Engineering at Columbia University. In 1996-97 he was a visiting Professor in the CESAM project at Spelman College. From 1973-1974 he was an associate editor of the IEEE Transactions on Automatic Controls. Barnes, whose research interests include Linear Algebra, and mathematical programming has published nearly 40 mathematics papers and is the co-author of a forthcoming book on linear programming. He is a Full Professor in the School of Industrial and Systems Engineering of Georgia Institute of Technology. He is a member of the board of CAARMS, the Council for African American Researchers in the Mathematical Sciences, SIAM, AMS, MAA, MPS, and INFORMS.

RESEARCH NOTES

Dr. Barnes has published nearly 40 papers in Mathematics. In particular, he is interested in interior point methods for linear programming problems, and in nonlinear approaches to certain combinatorial optimization problems. More details can be obtained from his publication web page: http://www.isye.gatech.edu/people/faculty/Earl_Barnes/publications.html

PUBLICATIONS

BOOKS

1. Wielandt, Helmut Mathematische Werke/Mathematical works. Vol. 2. Linear algebra and analysis. With essays on some of Wielandt's works by G. P. Barker, E. R. Barnes, J. von Below et al. Edited and with a preface by Bertram Huppert and Hans Schneider. Walter de Gruyter & Co., Berlin, 1996. xx+632 pp. ISBN: 3-11-012453-X

PAPERS

39. Barnes, Earl R. A lower bound for the chromatic number of a graph, Contemp. Math., 275, (2001) 3--12.

38 Castillo, Ileana; Barnes, Earl R. Chaotic behavior of the affine scaling algorithm for linear programming. SIAM J. Optim. 11 (2000), no. 3, 781--795 (electronic).

37.Barnes, Earl R. A branch-and-bound procedure for the largest clique in a graph. Approximation and complexity in numerical optimization, Nonconvex Optim. Appl. 42, 63--77.

36. Barnes, Earl R.; Moretti, Antonio Carlos A new characterization of the center of a polytope. Mat. Apl. Comput. 16 (1997), no. 3, 185--204.

35. Barnes, Earl R.An inequality for probability moments with applications, SIAM J. Discrete Math. 8 (1995), 347--358.

34. Barnes, E. R.; Hoffman, A. J. Bounds for the spectrum of normal matrices. Linear Algebra Appl. 201 (1994), 79--90.

33. Barnes, Earl R., A.J. Hoffman and Uriel G. Rothblum Optimal partitions having disjoint convex and conic hulls, Math. Programming 54 (1992), 69--86.)

32. Barnes, Earl R. Some results concerning convergence of the affine scaling algorithm. Mathematical developments arising from linear programming (Brunswick, ME, 1988), 131--139, Contemp. Math., 114, Amer. Math. Soc., Providence, RI, 1990.

31. Barnes, Earl R. Circular discs containing eigenvalues of normal matrices, Linear Algebra Appl. 114/115 (1989), 501--521.

30. Barnes, Earl R.; Vannelli, Anthony; Walker, James Q. A new heuristic for partitioning the nodes of a graph. SIAM J. Discrete Math. 1 (1988), no. 3, 299--305.

Dikin, I. I. Letter to the editor: "A variation on Karmarkar's algorithm for solving linear programming problems" [Math. Programming {\bf 36} (1986), no. 2, 174--182; MR 88h:90120] by E. R. Barnes. Math. Programming 41 (1988), no. 3 (Ser. A), 393--394.

29. Barnes, Earl R. Partitioning the nodes of a graph. Graph theory with applications to algorithms and computer science, 57--72, Wiley-Intersci. Publ., Wiley, New York, (1985).

28. Barnes, Earl R. A variation on Karmarkar's algorithm for solving linear programming problems. Math. Programming 36 (1986), no. 2, 174--182.

27. Barnes, Earl R. Partitioning the nodes of a graph. Graph theory with applications to algorithms and computer science (Kalamazoo, Mich., 1984), 57--72, Wiley-Intersci. Publ., Wiley, New York, 1985.

26. Barnes, Earl R.; Hoffman, Alan J. Partitioning, spectra and linear programming. Progress in combinatorial optimization (Waterloo, Ont., 1982), 13--25, Academic Press, Toronto, Ont., 1984.

25. Barnes, Earl R.; Hoffman, Alan J. On transportation problems with upper bounds on leading rectangles. SIAM J. Algebraic Discrete Methods 6 (1985), no. 3, 487--496.

24. Barnes, Earl R. A tribute to Professor Alexander Y. Lerner. IEEE Trans. Automat. Control 29 (1984), no. 10, 865.

23. Barnes, E. R. An algorithm for separating patterns by ellipsoids. IBM J. Res. Develop. 26 (1982), no. 6, 759--764.

22. Barnes, Earl R. An algorithm for partitioning the nodes of a graph . SIAM J. Algebraic Discrete Methods 3 (1982), no. 4, 541--550.

21. Barnes, E. R.; Hoffman, A. J. On bounds for eigenvalues of real symmetric matrices. Linear Algebra Appl. 40 (1981), 217--223.

20. Barnes, Earl R. Stability conditions for linear Hamiltonian systems with periodic coefficients . SIAM J. Math. Anal. 12 (1981), no. 1, 60--71.

19. Barnes, Earl R. Stability conditions for second-order ordinary differential equations with periodic coefficients . SIAM J. Math. Anal. 10 (1979), no. 5, 985--1001.

18. Barnes, Earl R. Dual variational inequalities for extremal eigenvalue problems . Control of distributed parameter systems (Proc. Second IFAC Sympos., Coventry, 1977), pp. 35--44, IFAC, Düsseldorf, 1978.

17. Leung-Yan-Cheong, Sik K.; Barnes, Earl R.; Friedman, Daniel U. On some properties of the undetected error probability of linear codes . IEEE Trans. Inform. Theory 25 (1979), no. 1, 110--112.

16. Barnes, Earl R. Stability conditions for second-order ordinary differential equations with periodic coefficients, SIAM J. Math. Anal. 10 (1979), 985--1001.

15. Barnes, Earl R. Some max-min problems arising in optimal design studies . Control theory of systems governed by partial differential equations (Conf., Naval Surface Weapons Center, Silver Spring, Md., 1976), pp. 177--208. Academic Press, New York, 1977.

14. Barnes, Earl R. Stability conditions for second order ordinary differential equations with periodic coefficients . Proceedings of the 1977 IEEE Conference on Decision and Control (New Orleans, La., 1977), Vol. 1, pp. 1256--1261. Inst. Electrical Electron. Engrs., New York, 1977.

13. Barnes, Earl R. The shape of the strongest column and some related extremal eigenvalue problems . Quart. Appl. Math. 34 (1976/77), no. 4, 393--409.

12. Barnes, Earl R. A variational problem arising in the design of cooling fins, Quart. Appl. Math. 34 (1976), 1--17.

11. Barnes, E. R.; Miranker, W. L. An application of optimal control theory to equation solving, Proceedings of the IEEE Conference on Decision and Control and the 15th Symposium on Adaptive Processes (Clearwater, Fla., 1976), pp. 543--547. Inst. Electr. Electron. Engrs., New York, 1976.

10. Barnes, Earl R. A variational problem arising in the design of cooling fins, Quart. Appl. Math. 34 (1976), no. 1, 1--17.

9. Barnes, E. R.; Russell, D. L. Totally implicit methods for numerical solution of singular initial value problems . Symposium on Ordinary Differential Equations (Univ. Minnesota, Minneapolis, Minn., 1972; dedicated to Hugh L. Turrittin), pp. 164--187. Lecture Notes in Math., Vol. 312, Springer, Berlin, 1973.

8. Barnes, E. R. Recent developments in control theory . Proceedings of the NSF Regional Conference on Control Theory held at the University of Maryland Baltimore County, Baltimore, Md., August 23--27, 1971. Edited by Nam P. Bhatia. Reprinted from SIAM J. Control {\bf 10} (1972), no. 2, 221--399. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1972. v+177 pp. 93-06

7. Barnes, Earl R. A procedure for solving certain dual optimal control problems, SIAM J. Control 10 (1972), 377--392.

6. Barnes, Earl R. Solution of a dual problem in optimal control theory . SIAM J. Control 11 (1973), 344--357.

5. Barnes, Earl R. A geometrically convergent algorithm for solving optimal control problems . SIAM J. Control 10 (1972), 434--443.

4. Barnes, Earl R. A procedure for solving certain dual optimal control problems . SIAM J. Control 10 (1972), 377--392.

3. Barnes, Earl R. Necessary and sufficient optimality conditions for a class of distributed parameter control systems . SIAM J. Control 9 1971 62--82.

2. Barnes, Earl R. An extension of Gilbert's algorithm for computing optimal controls, J. Optimization Theory Appl. 7 (1971), 420--443.

1. Barnes, Earl R. An extension of Gilbert's algorithm for computing optimal controls . J. Optimization Theory Appl. 7 (1971), 420--443.

BACK TO CONTENTS

The web pages
MATHEMATICIANS OF THE AFRICAN DIASPORA
are brought to you by


The Mathematics Department of
The State University of New York at Buffalo.

They are created and maintained by
Scott W. Williams
Professor of Mathematics

CONTACT Dr. Williams