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.

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