다음은 심도있는 최적화 학습을 위한 책과 논문 리스트입니다.

본 리스트의 도서 및 논문과 함께 ILOG R&D 팀이 작성한 최적화에 대한 테크니컬 페이퍼인ILOG R&D literature page를 참조하십시오

Textbooks

• Modeling
  
  H. Paul Williams, Model Building in Mathematical Programming, Wiley, 1999 (fourth edition)
  
  
• Constraint Programming
  
  Francesca Rossi, Peter van Beek, Toby Walsh ( ed). Handbook of Constraint Programming, Elsevier, 2006
  
  Philippe Baptiste, Claude Le Pape, Wim Nuijten, Constraint-Based Scheduling - Applying Constraint Programming to Scheduling Problems, Springer, 2001.
  
  
• Linear Programming
  
  Dantzig , George, Linear Programming and Extensions, Princeton University Press, 1963
  
  Vasek Chvatal, Linear Programming, W.H. Freeman and Company, 1983
  
  Nazareth , Larry, Computer Solution of Linear Programs, Oxford University Press, 1987.
  
  
• Integer Programming
  
  Nemhauser , George, and Wolsey, Laurence, Integer and Combinatorial Optimization, Wiley Interscience, 1988
  
  Wolsey, Laurence, Integer Programming, Wiley Interscience, 1998
  
  

Journal Articles

• Constraint Programming
  
  M. Wallace. Practical Applications of Constraint Programming. Constraints 1:139-168, 1996.
  
  A. Fernández, P. Hill.   A Comparative Study of Eight Constraint Programming Languages Over the Boolean and Finite Domains. Constraints 5:275-301, 2000.
  
  
• Linear Programming
  
  Forrest, J. J., D. Goldfarb. Steepest-edge simplex algorithms for linear programming. Math. Programming 57 (1992), 341-374.
  
  Gilbert, J. R., T. Peierls. Sparse partial pivoting in time proportional to arithmetic operations. SIAM J. Sci. Statist. Comput . 9 (1988), 862-874.
  
  Goldfarb, D. Using steepest-edge simplex algorithms to solve sparse linear programs. Sparse Matrix Computations. Academic Press, 1976, 227-240.
  
  Harris, P. M. J. Pivot selection methods of the devex LP code. Math. Programming 5 (1974), 1-28.
  
  Karmarkar , N. A new polynomial-time algorithm for linear programming. Combinatorica 4 (1984), 373-395.
  
  Suhl , U. H., L. M. Suhl. Computing sparse LU factorizations for large-scale linear programming bases. ORSA J. Computing (1990), 325-335.
  
  
• Quadratic Programming
  
  E. D. Andersen, C. Roos, and T. Terlaky, On implementing a primal-dual interior-point method for conic quadratic optimization.
  
  
• Integer Programming - General
  
  Land, A. and Powell, S., Computer codes for problems of integer programming, in P.L. Hammer, E.L. Johnson, and B.H. Korte, editors, Discrete Optimization II, Annals of Discrete Mathematics Volume 5, North Holland, Amsterdam, 1979, pages 221-269.
  
  Forrest, J., Hirst, J., and Tomlin J., Practical Solution of Large Mixed Integer Programming Problems with Umpire. Management Science, Volume 20, Number 5, January 1974, pages 736-772.
  
  Hoffman, K.L. and Padberg, M., (1985) LP-Based Combinatorial Problem Solving. Annals of Operations Research Volume 4, pages 145-194.
  
  
• Integer Programming - Branching
  
  J. T. Linderoth and M. W. P. Savelsbergh, "A Computational Study of Branch and Bound Search Strategies for Mixed Integer Programming," INFORMS Journal on Computing, 11 (1999) pp. 173-187.
  
  Tobias Achterberg, Thorsten Koch and Alexander Martin. "Branching rules revisited". Operations Research Letters, Volume 33, Issue 1 , January 2005, Pages 42-54
  
  
• Integer Programming - Heuristics
  
  Faaland , BH, FS Hillier. Interior path methods for heuristic integer programming procedures. Operations Research 27(6), 1979, pp. 1069–1087.
  
  Egon Balas, Sebastián Ceria, Milind Dawande, Francois Margot and Gábor Pataki. OCTANE: A New Heuristic for Pure 0-1 Programs. INFORMS Journal on Computing, Volume 49, Issue 2 (2001) pp. 207-225
  
  M. Fischetti, A. Lodi, “Local Branching”, Mathematical Programming B, 98, 23-47, 2003.
  
  M. Fischetti, F. Glover, A. Lodi, “The Feasibility Pump”, Mathematical Programming A, 104, 91-104, 2005.
  
  
• Integer Programming - Cuts
  
  R.E. Gomory, An algorithm for the mixed integer problem, Technical Report RM-2597, The RAND Cooperation, 1960.
  
  H. Crowder, E. Johnson, and M. W. Padberg, Solving large-scale zero-one linear programming problems, Operations Research 31, 803-834, 1983.
  
  E.L. Johnson, M.W. Padberg, Degree-two inequalities, clique facets, and biperfect graphs, Ann. Discrete Math. 16 (1982) 169-187.
  
  M.W. Padberg, T.J. Van Roy, L.A. Wolsey, Valid linear inequalities for fixed charge problems, Oper. Res. 33 (1985) 842-861.
  
  T. J. Van Roy , L. A. Wolsey, Solving mixed integer programming problems using automatic reformulation, Operations Research, v.35 n.1, p.45-57, Jan.-Feb. 1987
  
  Egon Balas , Sebastián Ceria , Gérard Cornuéjols, A lift-and-project cutting plane algorithm for mixed 0-1 programs, Mathematical Programming: Series A, v.58 n.3, p.295-324, Feb. 25, 1993
  
  E. Balas, S. Ceria, G. Cornuéjols, N. Natraj, Gomory cuts revisited, Oper. Res. Lett. 19 (1996) 1-9.
  
  A. Atamturk, G.L. Nemhauser, M.W.P. Savelsbergh, Conflict graphs in integer programming, European Journal of Operational Research 121, 40-55, 2000
  
  Hugues Marchand , Laurence A. Wolsey, Aggregation and Mixed Integer Rounding to Solve MIPs, Operations Research, v.49 n.3, p.363-371, May 2001
  
  Gerard Cornuejols, Yanjun Li and Dieter Vandenbussche. K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau. INFORMS Journal on Computing 15 (2003) 385-396.
  
  G. Codato, M. Fischetti, “Combinatorial Benders' Cuts” in Integer Programming and Combinatorial Optimization (proceedings of IPCO X), D. Bienstock and G. Nemhauser ed.s, Lecture Notes in Computer Science, Springer- Verlag Berlin Heidelberg, 178-195, 2004.
  
  Matteo Fischetti and Cristiano Saturni. Mixed-Integer Cuts from Cyclic Groups. Proceedings of IPCO XI. Springer Lecture Notes in Computer Science. Volume 3509 / 2005
  
  
• Integer Programming - Presolve
  
  Savelsbergh , M.W.P. (1994), Preprocessing and probing techniques for mixed integer programming problems. ORSA Journal on Computing, Volume 6, Number 4, pages 445-454.
  
  Andersen, E.D. and Andersen, K.D. (1995), Presolving in linear programming. Mathematical Programming Volume 71, pages 221-245.
  
  Brearley , A.L., Mitra, G., and Williams, H.P. (1975). Analysis of mathematical programming problems prior to applying the simplex algorithm. Mathematical Programming Volume 8, pages 54--83.
  
  
• Integer Programming - Probing
  
  Savelsbergh , M.W.P. (1994). Preprocessing and Probing for Mixed Integer Programming Problems, ORSA Journal on Computing, Volume 6, pages 445-454.
  
  
• Integer Programming - Other
  
  F. Margot, "Exploiting Orbits in Symmetric ILP", Mathematical Programming Ser. B 98 (2003), 3--21.