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Mathematics

Early research on non-linear differential equations was succeeded by a long period of work on linear and integer programming and on combinatorial problems.

Origin and Early Evolution of Corner Polyhedra European Journal of Operational Research, Volume 253, Issue 3, pages 543-556, (16 September 2016)

Forty Years of Corner Polyhedra Lecture, 12th Combinatorial Optimization Workshop, Aussois, France, January 8, 2008

Corner Polyhedra Lecture, George Nemhauser Symposium, Georgia Tech, June 26-27, 2007

Thoughts About Integer Programming Lecture,  University of Montreal, January 26, 2007

The Atoms of Integer Programming Annals of Operations Research. 149, pp. 99–102 (2007)

Cyclic Group and Knapsack Facets Julian Araoz, Lisa Evans, Gomory, R. E., Johnson, E. L. Mathematical Programming. Ser.B 96: Springer-Verlag, pp. 377-408 (2003).

Corner Polyhedra and their Connections with Cutting Planes Gomory, R. E., Johnson, E.L. Lisa Evans. Mathematical Programming. Ser.B 96: Springer-Verlag, pp. 321-339 (2003).

T-space and Cutting Planes Gomory, R. E., Johnson, E.L. Mathematical Programming. Ser. B 96: Springer-Verlag, pp. 341-375 (2003).

Delays at Toll Booths – Why Wait in Line? (with Denos C. Gazis), Transportation Quarterly. Spring 1994, Vol 48, No. 2, pp. 107-114.

Early Integer Programming History of Mathematical Programming. Edited by J. K. Lenstra, A. H. G. Rinnooy Kan, and A. Schrijver, Elsevier Science Publishers B.V., Amsterdam, 1991, pp. 55-61.

Multi-Terminal Flows in a Network (with T. C. Hu), Studies in Graph Theory, Vol. 11, Part 1, edited by D. R. Fulkerson, The Mathematical Association of America, 1975, pp. 172-199.

R-Separating Sets (with T.C. Hu and J. M. Yohe), Canadian Journal of Mathematics, Vol. XXVI, No. 6. 1974, pp. 1418-1429.

The Group Problems and Subadditive Functions (with Ellis L. Johnson), Mathematical Programming. Academic Press, 1973, pp. 157-184.

Some Continuous Functions Related to Corner Polyhedra, Part II (with Ellis L. Johnson), Mathematical Programming, Vol. 3, No. 3. North-Holland, December 1972, pp. 359-389.

Some Continuous Functions Related to Corner Polyhedra, Part I (with Ellis L. Johnson), Mathematical Programming, Vol. 3, No. 1. North-Holland, August 1972, pp. 23-85.

Properties of a Class of Integer Polyhedra Integer and Non-Linear Programming. Edited by J. Abadie. North-Holland, 1970, pp. 353-365.

Some Polyhedra Related to Combinatorial Problems Journal of Linear Algebra and Its Applications, Vol. 2, No. 4. October 1969, pp. 451-558; also published in Combinatorial Structures and Their Applications, Proceedings of the Calgary International Conference on Combinatorial Structures and their Applications, held at the University of Calgary, Calgary, Alberta, Canada, June 1969. New York, Gordon and Breach, 1970, p. 117.

Flows in Continua  Sildenafil citrate Integer Programming and Network Flows, Chapter 12 (with T. C. Hu). Addison-Wesley Publishing Co., 1969, pp. 214-228.

Post-Doctoral Experience Proceedings of Conference on Education in Applied Mathematics sponsored by SIAM under a grant of NSF, Aspen, Colorado, May 24-27 1966, SIAM Review, Vol. 9, No. VI. April 1967, pp. 388-396 (discussion pp. 396-410).

Faces of an Integer Polyhedron Proceedings of the National Academy of Sciences, Vol. 57, No. 1. January 1967, pp.16-18; also published in Lectures in Applied Mathematics 2, Part I, Mathematics of the Decision Sciences. Ed. by G. B. Dantzig and A.F.Veinott, Jr., American Mathematical Society, 1968, pp. 283-287.

The Theory and Computation of Knapsack Functions (with P. C. Gilmore), Operations Research, Vol. 14, No. 6. November-December 1966, pp. 1045-1074.

On the Relation Between Integer and Non-Integer Solutions To Linear Programs Proceedings of the National Academy of Sciences, Vol. 53, No. 2. February 1965, pp.260-265; also published in Lectures in Applied Mathematics, 2, Part I, Mathematics of the Decision Sciences. Ed. by G. B. Dantzig and A. F. Veinott, Jr., American Mathematical Society, 1968, pp. 288-294.

Optimal Programming of Lot Sizes, Inventories and Labor Allocations (with B. P. Dzielinski),  Management Sciences, Vol. 11, No. 9. July 1965, pp. 874-890.

The Traveling Salesman Problem Proceedings of IBM , Scientific Computing Symposium on Combinatorial Problems, March 1964, IBM Data Processing Division (White Plains, NY), 1966, pp. 93-121.

Mathematical Programming American Mathematical Monthly, Vol. 72, No. 2. Pt. 2. February 1965, pp. 99-110.

Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem (with P. C. Gilmore), Operations Research, Vol. 12, No. 5. September-October 1964, pp. 655-679.

Multi-Stage Cutting Stock Problems of Two and More Dimensions (with P. C. Gilmore), Operations Research, Vol.13, No. 1. January-February 1965, pp. 94-120.

Automatic Design of Optimal Structures with W. S. Dorn and H. J. Greenberg), Journal de Mecanique, Vol. 3, No. 1. March 1964, pp. 25-52.

A Solvable Case of the Traveling Salesman Problem (with P. C. Gilmore), Proceedings of the National Academy of Sciences, Vol. 51, No. 2. February 1964, pp. 178-181.

A Linear Programming Approach to the Cutting Stock Problem — Part II (with P. C. Gilmore), Operations Research, Vol.11, No.6. November-December, 1963, pp. 863-888.

Some Properties of the Rank and Invariant Factors of Matrices (with A. J. Hoffman and N. C. Hsu), Canadian Mathematical Bulletin, Vol. 7, No. 1. January 1964, pp. 85-96.

Synthesis of a Communication Network (with T. C. Hu), SIAM Journal, Vol. 12, No. 2. June 1964, pp. 348-369.

Analysis and Synthesis of Communication Networks (with R. T. Chien and T. C. Hu), IEEE Transactions on Circuit Theory, Vol. CT-11, No. 1, March 1964, pp. 19-22.

A Primal Method for the Assignment and Transportation Problems (with Michel L. Balinski), Management Science, Vol. 10, No. 3. April 1964, pp. 578-593.

Large and Non-Convex Problems in Linear Programming Proceedings of the Symposium on the Interactions between Mathematical Research and High-Speed Computing of the American Mathematical Society, Vol. XV. 1963, pp. 125-139.

An Algorithm for Integer Solutions to Linear Programs Recent Advances in Mathematical Programming. Edited by Robert L. Graves and Philip Wolfe, McGraw-Hill, 1963, pp. 269-302.

All-Integer Integer Programming Algorithm Industrial Scheduling. Edited by John F. Muth and Gerald L. Thompson, Prentice-Hall, 1963, pp. 193-206.

A Mutual-Primal-Dual Simplex Method (with Michel L.Balinski), Proceedings of Mathematical Programming Symposium, 1963, pp. 17-26.

On the Convergence of an Integer-Programming Process (with A. J. Hoffman), Naval Research Logistics Quarterly, Vol. 10, No. 2. June 1963, pp. 121-123.

The Trim Problem IBM Systems Journal, September 1962, pp. 77-82.

“Finding Optimum Combinations,” (with A. J. Hoffman), Inter-national Science and Technology, July 1962, pp. 26-33.

An Application of Generalized Linear Programming to Network Flows (with T. C. Hu), Journal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 2. June 1962, pp. 260-283.

Multi-Terminal Network Flows (with T. C. Hu), Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 4. December 1961, pp. 551-570.

A Linear Programming Approach to the Cutting Stock Problem (with P. C. Gilmore), Operations Research, Vol. 9, No. 6. November-December 1961, pp. 849-859.

Integer Programming and Pricing (with William J. Baumol), Econometrica, Vol. 28, No. 3. July 1960, pp. 521-550.

Solving Linear Programming Problems in Integers Proceedings of Symposia in Applied Mathematics, Vol. 10. July 1960, pp. 211-215.

Outline of an Algorithm for Integer Solutions to Linear Programs Bulletin of the American Mathematical Society, Vol. 64, No. 5. September 1958, pp. 275-278.

Critical Points at Infinity and Forced Oscillation Contributions to the Theory of non-Linear Oscillations, Vol. 3, Annals of Mathematics, Study 36. Princeton University Press, 1956, pp. 85-126.

A Study of Trajectories Which Tend to a Limit Cycle in 3-Space (with F. Haas), Annals of Mathematics, Vol. 62, No. 1. July 1955, pp. 152-161.

Trajectories Tending to a Critical Point in 3-Space Annals of Mathematics, Vol. 61, No. 1. January 1955, pp.140-153.

Boundaries for the Limit-Cycle of Van der Pol’s Equation (with D. E. Richmond), Quarterly of Applied Mathematics,Vol. IX, No. 2. July 1951, pp. 205-209.