Dept. of Industrial Engineering & Management Sciences
Northwestern University
tel: 847/491-3151
fax: 847/467-1828, 847/491-8005
4er@iems.nwu.edu
s-mail: Dept. of Industrial Engineering & Management Sciences
Northwestern University
2225 North Campus Drive
Evanston, IL 60208-3119, U.S.A.
http://www.iems.nwu.edu/~4er
Research Interests
- The AMPL modeling language and system for large-scale linear, integer, and nonlinear programming, in collaboration with David Gay and Brian Kernighan of Bell Laboratories. Ongoing projects include extensions for complementarity problems, for database access, and for a more flexible interface with solvers generally.
- General-purpose modeling systems for combinatorial optimization, in collaboration with Prof. Collette Coullard of Northwestern University. Projects include extensions of AMPL for combinatorial problems, and the GIDEN modeling environment for network-based optimization.
- Guide for Prospective Doctoral Students in Industrial Engineering and Management Sciences at Northwestern University.
Recent Papers and Reports:
Presentations
Copies of transparencies for the following talks are available in PDF, postscript, and gzip-compressed postscript formats.
Tutorials & Surveys
R. Fourer, On-Line Optimization Services, from Panel on The OR/MS-WWW Interface, Session TC03, INFORMS Israel International Meeting, Tel Aviv, June 30, 1998.
R. Fourer, Tutorial: Software for Linear and Integer Programming, Session TC19, CORS/INFORMS Meeting, Montreal, April 28, 1998.
R. Fourer, Implications of Constraint Logic Programming for the Design of Mathematical Programming Systems, Tutorial TC3, INFORMS CSTS Conference, Monterey, CA, January 8, 1998.
Modeling
R. Fourer and D.M. Gay, New Directions in Algebraic Modeling Languages, Session MC04.3, INFORMS National Meeting, Seattle, October 26, 1998.
R. Fourer, Recent Developments in Mathematical Programming Modeling Systems, OR40: Conference of the Operational Research Society, Lancaster, England, September 8, 1998.
R. Fourer, Optimization Approaches to Production Planning in the Steel Industry, Association of Iron and Steel Engineers Specialty Conference, Advanced Technologies in Modeling, Scheduling and Control, M.I.T., Cambridge, MA, July 22, 1998.
AMPL
R. Fourer and D.M. Gay, Updating the AMPL/Solver Interface, Session TD1.2, APMOD ’98, Limassol, Cyprus, March 12, 1998.
R. Fourer, and D.M. Gay, Analysis Support in a Modeling Language for Mathematical Programming, Session WB1, INFORMS CSTS Conference, Monterey, CA, January 7, 1998.
R. Fourer and D.M. Gay, Proposals for Stochastic Programming in the AMPL Modeling Language,
Session WE4-G-IN11, International Symposium on Mathematical Programming, Lausanne, August 27,
1997.
R. Fourer, Uses of the AMPL Modeling Language in Solving “Balanced” Assignment Problems, Session TC24.3, EURO/INFORMS International Meeting, Barcelona, July 15, 1997.
Combinatorial Optimization
R. Fourer, C.R. Coullard and J.H. Owen, General-Purpose Algorithms & Systems for Combinatorial Optimization, Session MA14, INFORMS International Meeting, Tel Aviv, June 29, 1998.
R. Fourer, General-Purpose Modeling Languages for Combinatorial Optimization, Session WC1.1, APMOD ’98, Limassol, Cyprus, March 11, 1998.
Writings
Books
R. Fourer, D.M. Gay, and B.W. Kernighan, AMPL: A Modeling Language for Mathematical Programming. Duxbury Press, Belmont, CA (1993).
Reports Available On-Line
R. Fourer, Software for Optimization: A Survey of Recent Trends in Mathematical Programming Systems. OR/MS Today 25:6 (December 1998) 40-43.
M.C. Ferris, R. Fourer and D.M. Gay, Expressing Complementarity Problems in an Algebraic Modeling Language and Communicating Them to Solvers. Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University (1998).
R. Fourer, Software Survey: Linear Programming. OR/MS Today 24:2 (April 1997) 54-55.
R. Fourer, Software for Optimization: A Buyer’s Guide. Part 1, INFORMS Computer Science Technical Section Newsletter 17:1 (1996) 1, 14-17. Part 2, INFORMS Computer Science Technical Section Newsletter 17:2 (1996) 3-4, 9-10.
C. Coullard and R. Fourer, Interdependence of Methods and Representations in Design of Software for Combinatorial Optimization. Technical Report 95-67, Department of Industrial Engineering and Management Sciences, Northwestern University (1995); presented at the First International Joint Workshop on Artificial Intelligence and Operations Research, Timberline, OR (1995).
R. Fourer, Notes on the Dual Simplex Method. Draft report (1994).
R.E. Bixby and R. Fourer, Finding Embedded Network Rows in Linear Programs II: Augmentation Heuristics. Preliminary draft report (1987).
Published Articles
R. Fourer, Extending a General-Purpose Algebraic Modeling Language to Combinatorial Optimization: A Logic Programming Approach. In D.L. Woodruff, ed., Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search: Interfaces in Computer Science and Operations Research, Kluwer Academic Publishers, Dordrecht, The Netherlands (1998) 31-74.
J. Czyzyk, R. Fourer and S. Mehrotra, Using a Massively Parallel Processor to Solve Large Sparse Linear Programs by an Interior-Point Method. SIAM Journal on Scientific Computing 19 (1998) 553-565.
R. Fourer, Database Structures for Mathematical Programming Models. Decision Support Systems 20 (1997) 317-344.
J.J. Bisschop and R. Fourer, New Constructs for the Description of Combinatorial Optimization Problems in Algebraic Modeling Languages. Computational Optimization and Applications 6 (1996) 83-116.
J. Czyzyk, R. Fourer and S. Mehrotra, A Study of the Augmented System and Column-Splitting Approaches for Solving Two-Stage Stochastic Linear Programs by Interior-Point Methods. ORSA Journal on Computing 7 (1995) 474-490.
R. Fourer and D.M. Gay, Expressing Special Structures in an Algebraic Modeling Language for Mathematical Programming. ORSA Journal on Computing 7 (1995) 166-190.
R. Fourer and D.M. Gay, Experience with a Primal Presolve Algorithm. In Large Scale Optimization: State of the Art, W.W. Hager, D.W. Hearn and P.M. Pardalos, eds., Kluwer Academic Publishers (Dordrecht, 1994) 135-154.
R. Fourer and S. Mehrotra, Solving Symmetric Indefinite Systems in an Interior-Point Method for Linear Programming. Mathematical Programming 62 (1993) 15-39.
R. Fourer and R.E. Marsten, Solving piecewise-linear programs: Experiments with a simplex approach. ORSA Journal on Computing 4 (1992) 16-31.
R. Fourer, A Simplex Algorithm for Piecewise-Linear Programming, III: Computational Analysis and Applications. Mathematical Programming 53 (1992) 213-235.
R. Fourer, D.M. Gay, and B.W. Kernighan, A Modeling Language for Mathematical Programming. Management Science 36 (1990) 519-554.
R. Fourer, A Simplex Algorithm for Piecewise-Linear Programming, II: Finiteness, Feasibility and Degeneracy. Mathematical Programming 41 (1988) 281-315.
R.E. Bixby and R. Fourer, Finding Embedded Network Rows in Linear Programs I: Extraction Heuristics. Management Science 34 (1988) 342-376.
R. Fourer, A Simplex Algorithm for Piecewise-Linear Programming, I: Derivation and Proof. Mathematical Programming 33 (1985) 204-233.
R. Fourer, Staircase Matrices and Systems. SIAM Review 26 (1984) 1-70.
R. Fourer, Modeling Languages versus Matrix Generators for Linear Programming. ACM Transactions on Mathematical Software 9 (1983) 143-183.
R. Fourer, Solving Staircase Linear Programs by the Simplex Method, 2: Pricing. Mathematical Programming 25 (1983) 251-292.
R. Fourer, Solving Staircase Linear Programs by the Simplex Method, 1: Inversion. Mathematical Programming 23 (1982) 274-313.
R. Fourer, J.B. Gertler and H.J. Simkowitz, Optimal Fleet Sizing and Allocation for Improved Rail Service in the Northeast Corridor. Transportation Research Record 656 (1978) 40-45.
R. Fourer, J.B. Gertler and H.J. Simkowitz, Models of Railroad Passenger-Car Requirements in the Northeast Corridor. Annals of Economic and Social Measurement 6 (1977) 367-398.