On generalized geometric programming problems with non-positive variables

European Journal of Operational Research

Volumn 178, Issue 1, 2007, Pages 10-19

  Tsai, Jung Fa ^a   Lin, Ming Hua ^b   Hu, Yi Chung ^c  

^a NATIONAL TAIPEI UNIVERSITY OF TECHNOLOGY   (Taiwan)

^b SHIH CHIEN UNIVERSITY   (Taiwan)

^c CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

Author keywords

Convexification; Generalized geometric programming; Global optimization; Non positive variables

Indexed keywords

COMPUTATION THEORY; GLOBAL OPTIMIZATION; MATHEMATICAL PROGRAMMING; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

CONVEXIFICATION; GENERALIZED GEOMETRIC PROGRAMMING (GGP); NON-POSITIVE VARIABLES;

COMPUTATIONAL GEOMETRY;

EID: 33750814653     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2005.11.037     Document Type: Article

References (22)

1. Avriel M., and Williams A.C. Complementary geometric programming. SIAM Journal on Applied Mathematics 19 1 (1970) 125-141
2. Björk K.-M., Lindberg P.O., and Westerlund T. Some convexifications in global optimization of problems containing signomial terms. Computers and Chemical Engineering 27 (2003) 669-679
3. Duffin R.J., and Peterson E.L. Reversed geometric programming treated by harmonic means. Indian University Mathematics Journal 22 (1972) 531-550
4. Floudas C.A., and Visweswaran V. Quadratic optimization. In: Horst R., and Pardalos P.M. (Eds). Handbook of Global Optimization, Nonconvex Optimization and its Applications (1994), Kluwer Academic Publishers 217-270
5. Floudas C.A., Pardalos P.M., Adjiman C.S., Esposito W.R., Gumus Z., Harding S.T., Klepeis J.L., Meyer C.A., and Schweiger C.A. Handbook of Test Problems in Local and Global Optimization (1999), Kluwer Academic Publishers, Boston
6. Floudas C.A. Deterministic Global Optimization: Theory, Methods and Application (2000), Kluwer Academic Publishers, Boston
7. Horst R., and Tuy H. Global Optimization: Deterministic Approaches (1996), Springer-Verlag, Berlin, Germany
8. Kortanek K.O., Xu X., and Ye Y. An infeasible interior-point algorithm for solving primal and dual geometric programs. Mathematical Programming 76 1 (1997) 155-181
9. LINGO Release 9.0: Lindo System Inc., 2004.
10. Maranas C.D., and Floudas C.A. Global optimization in generalized geometric programming. Computers and Chemical Engineering 21 4 (1997) 351-370
11. Passy U., and Wilde D.J. Generalized polynomial optimization. SIAM Journal on Applied Mathematics 15 5 (1967) 1344-1356
12. Passy U. Generalized weighted mean programming. SIAM Journal on Applied Mathematics 20 4 (1971) 763-778
13. Pörn R., Harjunkoski I., and Westerlund I.T. Convexification of different classes of non-convex MINLP problems. Computers and Chemical Engineering 23 (1999) 439-448
14. Ryoo H.S., and Sahinidis N.V. Global optimization of nonconvex NLPs and MINLPs with applications in process design. Computers and Chemical Engineering 19 5 (1995) 551-566
15. Shen P., and Zhang K. Global optimization of signomial geometric programming using linear relaxation. Applied Mathematics and Computation 150 1 (2004) 99-114
16. Sherali H.D., and Tuncbilek C.H. A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique. Journal of Global Optimization 2 (1992) 101-112
17. Sherali H.D., and Tuncbilek C.H. A reformulation-convexification approach for solving nonconvex quadratic programming problems. Journal of Global Optimization 7 (1995) 1-31
18. Sherali H.D. Global optimization of nonconvex polynomial programming problems having rational exponents. Journal of Global Optimization 12 (1998) 267-283
19. T. Westerlund, K.-M. Björk, A class of transformations convexifying and underestimating positive signomial terms, Report 02-183-A, Process Design Laboratory at Abo Akademi University, Finland, ISBN 952-12-1018-4, 2002.
20. T. Westerlund, K.-M. Björk, A class of transformations convexifying and underestimating negative signomial terms, Report 02-182-A, Process Design Laboratory at Abo Akademi University, Finland, ISBN 952-12-0968-2, 2002.
21. Westerlund T. Some transformation techniques in global optimization. In: Liberti L., and Maculan N. (Eds). Global Optimization. From Theory to Implementations (2005), Kluwer Academic Publishers 45-74
22. Yang H.H., and Bricker D.L. Investigation of path-following algorithms for signomial geometric programming problems. European Journal of Operational Research 103 1 (1997) 230-241