Convex relaxation for solving posynomial programs

Journal of Global Optimization

Volumn 46, Issue 1, 2010, Pages 147-154

  Lu, Hao Chun ^a   Li, Han Lin ^b   Gounaris, Chrysanthos E ^c   Floudas, Christodoulos A ^c  

^a FU JEN CATHOLIC UNIVERSITY   (Taiwan)

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

^c Princeton University   (United States)

Author keywords

Convex underestimation; Posynomial functions

Indexed keywords

CONVEX RELAXATION; LOGARITHMIC TRANSFORMATIONS; NONLINEAR FUNCTIONS; POSYNOMIAL; POSYNOMIAL FUNCTION;

RELAXATION PROCESSES;

GLOBAL OPTIMIZATION;

EID: 72449165495     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-009-9414-2     Document Type: Article

References (23)

1. I.G. Akrotirianakis C.A. Floudas 2004 Computational experience with a new class of convex underestimators: box constrained NLP problems J. Glob. Optim. 29 249 264 10.1023/B:JOGO.0000044768.75992.10 10.1023/B:JOGO.0000044768.75992.10
2. I.G. Akrotirianakis C.A. Floudas 2004 A new class of improved convex underestimators for twice continuously differentiable constrained NLPs J. Glob. Optim. 30 367 390 10.1007/s10898-004-6455-4 10.1007/s10898-004-6455-4 (Pubitemid 40308453)
3. Brooke A., Kendrick D., Meeraus A., Raman R.: GAMS: a users guide. GAMS Development Corporation, Washington, DC (2005)
4. K.J. Björk P.O. Lindberg T. Westerlund 2003 Some convexifications in global optimization of problems containing signomial terms Comput. Chem. Eng. 27 669 679 10.1016/S0098-1354(02)00254-5 10.1016/S0098-1354(02)00254-5 (Pubitemid 36433192)
5. S. Caratzoulas C.A. Floudas 2005 A trigonometric convex underestimator for the base functions in Fourier space J. Optim. Theory Appl. 124 339 362 10.1007/s10957-004-0940-2 10.1007/s10957-004-0940-2 (Pubitemid 40900315)
6. J. Czyzyk M. Mesnier J. More 1998 The NEOS server IEEE J. Comput. Sci. Eng. 5 68 75 10.1109/99.714603 10.1109/99.714603
7. Drud A.S.: CONOPT: a system for large-scale nonlinear optimization. Reference manual for CONOPT subroutine library. ARKI Consulting and Development A/S, Bagsvaerd, Denmark (1996)
8. C.A. Floudas 2000 Global optimization in design and control of chemical process systems J. Process Control 20 125 134 10.1016/S0959-1524(99)00019-0 10.1016/S0959-1524(99)00019-0 (Pubitemid 30556710)
9. C.A. Floudas I.G. Akrotirianakis S. Caratzoulas C.A. Meyer J. Kallrath 2005 Global optimization in the 21st century: advances and challenges Comput. Chem. Eng. 29 1185 1202 10.1016/j.compchemeng.2005.02.006 10.1016/j.compchemeng. 2005.02.006 (Pubitemid 40633581)
10. C.E. Gounaris C.A. Floudas 2008 Tight convex underestimators for C2-continuous problems: I Univariate functions. J. Glob. Optim. 42 51 67 10.1007/s10898-008-9287-9
11. C.E. Gounaris C.A. Floudas 2008 Tight convex underestimators for C2-continuous problems: II Multivariate functions. J. Glob. Optim. 42 69 89
12. Hamed, A.S.E.: Calculation of bounds on variables and underestimating convex functions for nonconvex functions. Ph.D thesis. The George Washington University (1991)
13. H.L. Li J.F. Tsai C.A. Floudas 2008 Convex Underestimation for Posynomial Functions of Positive Variables Optim. Lett. 2 333 340 10.1007/s11590-007-0061- 6 (Pubitemid 351653785)
14. L. Liberti C.C. Pantelides 2003 Convex envelops of monomials of odd degree J. Glob. Optim. 25 157 168 10.1023/A:1021924706467 10.1023/A: 1021924706467
15. C.D. Maranas C.A. Floudas 1995 Finding all solutions of nonlinearly constrained systems of equations J. Glob. Optim. 7 143 182 10.1007/BF01097059 10.1007/BF01097059
16. C.D. Maranas C.A. Floudas 1997 Global optimization in generalized geometric programming Comput. Chem. Eng. 21 351 370 10.1016/S0098-1354(96)00282- 7 10.1016/S0098-1354(96)00282-7
17. Meyer, C.A., Floudas, C.A.: Trilinear monomials with positive or negative domains: facets of the convex and concave envelopes. In : Floudas, C.A., Pardalos, P.M. (eds.) Frontiers in Global Optimization. Kluwer Academic Publishers, Santorini, Greece (2003)
18. C.A. Meyer C.A. Floudas 2004 Trilinear monomials with mixed sign domains: facets of the convex and concave envelopes J. Glob. Optim. 29 125 155 10.1023/B:JOGO.0000042112.72379.e6 10.1023/B:JOGO.0000042112.72379.e6
19. C.A. Meyer C.A. Floudas 2005 Convex envelopes for edge concave functions Math. Program. Ser. B. 103 207 224 10.1007/s10107-005-0580-9 10.1007/s10107-005-0580-9 (Pubitemid 40878748)
20. R. Pörn I. Harjunkoski T. Westerlund 1999 Convexification of different classes of non-convex MINLP problems Comput. Chem. Eng. 23 439 448 10.1016/S0098-1354(98)00305-6 10.1016/S0098-1354(98)00305-6 (Pubitemid 29179700)
21. H.S. Ryoo N.V. Sahinidis 2001 Analysis of bounds for multilinear functions J. Glob. Optim. 19 403 424 10.1023/A:1011295715398 10.1023/A:1011295715398 (Pubitemid 33672346)
22. Tardella F.: On the existence of polyhedral convex envelopes. In: Floudas, C.A., Pardalos, P.M. (eds) Frontiers in Global Optimization, pp. 563-573. Kluwer Academic Publishers, Santorini, Greece (2003)
23. Tawarmalani, M., Sahinidis, N.V.: BARON 7.2.5: Global optimization of mixed-integer nonlinear programs, User's manual (2005)