Base-2 expansions for linearizing products of functions of discrete variables

Operations Research

Volumn 60, Issue 6, 2012, Pages 1477-1490

  Adams, Warren P ^a   Henry, Stephen M ^b  

^a CLEMSON UNIVERSITY   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Nonlinear; Programming: integer; Theory

Indexed keywords

BINARY REALIZATIONS; BINARY VARIABLES; CONTINUOUS VARIABLES; DISCRETE VARIABLES; LINEARIZATION METHODS; MIXED-INTEGER; NONLINEAR; NONLINEAR PROGRAMS; THEORY; UNIVARIATE FUNCTIONS;

COMPUTER APPLICATIONS; OPERATIONS RESEARCH;

INTEGER PROGRAMMING;

EID: 84871866274     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1120.1106     Document Type: Article

References (17)

1. Adams WP, Forrester RJ (2005) A simple recipe for concise mixed 0-1 linearizations. Oper. Res. Lett. 33(1):55-61.
2. Bergamini ML, Scenna NJ, Aguirre PA (2007) Global optimal structures of heat exchanger networks by piecewise relaxation. Indust. Engrg. Chemistry Res. 46(6):1752-1763. (Pubitemid 46473455)
3. Boyd SP, Kim SJ, Patil DD, Horowitz MA (2005) Digital circuit optimization via geometric programming. Oper. Res. 53(6):899-932. (Pubitemid 43061808)
4. Floudas CA, Gounaris CE (2009) A review of recent advances in global optimization. J. Global Optim. 45(1):3-38.
5. Glover F (1975) Improved linear integer programming formulations of nonlinear integer programs. Management Sci. 22(4):455-460.
6. Glover F (1984) An improved MIP formulation for products of discrete and continuous variables. J. Inform. Optim. Sci. 5(1):469-471.
7. Harjunkoski I, Westerlund T, Pörn R (1999) Numerical and environmental considerations on a complex industrial mixed integer nonlinear programming (MINLP) problem. Comput. Chemical Engrg. 23(10):1545-1561.
8. Kallrath J (2003) Exact computation of global minima of a noncovex portfolio optimization problem. Floudas CA, Pardalos PM, eds. Frontiers in Global Optimization (Kluwer Academic Publishers, Boston), 237-254.
9. Li HL, Lu HC (2009) Global optimization for generalized geometric programs with mixed free-sign variables. Oper. Res. 57(3):701-713.
10. Li HL, Lu HC, Huang CH, Hu NZ (2009) A superior representation method for piecewise linear functions. INFORMS J. Comput. 21(2):314-321.
11. Meyer CA, Floudas CA (2006) Global optimization of a combinatorially complex generalized pooling problem. Amer. Inst. Chemical Engineers J. 52(3):1027-1037.
12. Sahinidis NV, Tawarmalani M (2000) Applications of global optimization to process and molecular design. Comput. Chemical Engrg. 24(9-10):2157-2169.
13. Sinha M, Achenie L E K, Ostrovsky GM (1999) Environmentally benign solvent design by global optimization. Comput. Chemical Engrg. 23(10):1381-1394.
14. Vielma JP, Nemhauser GL (2011) Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Math. Programming 128(1-2):49-72.
15. Vielma JP, Ahmed S, Nemhauser GL (2010a) A note on "A superior representation method for piecewise linear functions." INFORMS J. Comput. 22(3):493-497.
16. Vielma JP, Ahmed S, Nemhauser GL (2010b) Mixed-integer models for nonseparable piecewise-linear optimization: Unifying framework and extensions. Oper. Res. 58(2):303-315.
17. Watters LJ (1967) Reduction of integer polynomial programming problems to zero-one linear programming problems. Oper. Res. 15(6):1171-1174.