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A robust algorithm for generalized geometric programming. (English) Zbl 1152.90613
Summary: Most existing methods of global optimization for generalized geometric programming (GGP) actually compute an approximate optimal solution of a linear or convex relaxation of the original problem. However, these approaches may sometimes provide an infeasible solution, or far from the true optimum. To overcome these limitations, a robust solution algorithm is proposed for global optimization of (GGP) problem. This algorithm guarantees adequately to obtain a robust optimal solution, which is feasible and close to the actual optimal solution, and is also stable under small perturbations of the constraints.

MSC:
90C30Nonlinear programming
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References:
[1] Avriel M. and Williams A.C. (1971). An extension of geometric programming with applications in engineering optimization. J. Eng. Math. 5(3): 187--199 · doi:10.1007/BF01535411
[2] Jefferson T.R. and Scott C.H. (1978). Generalized geometric programming applied to problems of optimal control: I. Theory. J. Optim. Theory Appl. 26: 117--129 · Zbl 0369.90120 · doi:10.1007/BF00933274
[3] Nand K.J. (1995). Geometric programming based robot control design. Comput. Indust. Eng. 29(1--4): 631--635 · doi:10.1016/0360-8352(95)00146-R
[4] Das K., Roy T.K. and Maiti M. (2000). Multi-item inventory model with under imprecise objective and restrictions: a geometric programming approach. Production Plan. Control 11(8): 781--788 · doi:10.1080/095372800750038382
[5] Jae Chul C. and Bricker Dennis L. (1996). Effectiveness of a geometric programming algorithm for optimization of machining economics models. Comput. Oper. Res. 23(10): 957--961 · Zbl 0873.90043 · doi:10.1016/0305-0548(96)00008-1
[6] EI Barmi H. and Dykstra R.L. (1994). Restricted multinomial maximum likelihood estimation based upon Fenchel duality. Stat. Probab. Lett. 21: 121--130 · Zbl 0801.62033 · doi:10.1016/0167-7152(94)90219-4
[7] Bricker D.L., Kortanek K.O. and Xu L. (1995). Maximum Likelihood Estimates with Order Restrictions on Probabilities and Odds Ratios: A Geometric Programming Approach. Applied Mathematical and Computational Sciences, the University of IA, Iowa City, IA · Zbl 0953.62027
[8] Jagannathan R. (1990). A stochastic geometric programming problem with multiplicative recourse. Oper. Res. Lett. 9: 99--104 · Zbl 0703.90069 · doi:10.1016/0167-6377(90)90048-A
[9] Sönmez A.I., Baykasoglu A., Dereli T. and Filiz I.H. (1999). Dynamic optimization of multipass milling operations via geometric programming. Int. J. Machine Tools Manuf. 39: 297--320 · doi:10.1016/S0890-6955(98)00027-3
[10] Scott C.H. and Jefferson T.R. (1995). Allocation of resources in project management. Int. J. Syst. Sci. 26: 413--420 · Zbl 0821.90069 · doi:10.1080/00207729508929042
[11] Maranas C.D. and Floudas C.A. (1997). Global optimization in generalized geometric programming. Comput. Chem. Eng. 21(4): 351--369 · doi:10.1016/S0098-1354(96)00282-7
[12] Rijckaert M.J. and Martens X.M. (1974). Analysis and optimization of the Williams-Otto process by geometric programming. AICHE J 20(4): 742--750 · doi:10.1002/aic.690200416
[13] Shen P. and Zhang K. (2004). Global optimization of signomial geometric programming using linear relaxation. Appl. Math. Comput. 150: 99--114 · Zbl 1053.90112 · doi:10.1016/S0096-3003(03)00200-5
[14] Wang Y., Zhang K. and Gao Y. (2004). Global optimization of generalized geometric programming. Comput. Math. Appl. 48: 1505--1516 · Zbl 1066.90096 · doi:10.1016/j.camwa.2004.07.008
[15] Tuy H. (2005). Robust solution of nonconvex global optimization problems. J. Glob. Optim. 32: 357--374 · Zbl 1123.90059
[16] Tuy H. (2000). Monotonic optimization: problems and solution approaches. SIAM J. Optim. 11(2): 464--494 · Zbl 1010.90059 · doi:10.1137/S1052623499359828
[17] Tuy H., Al-Khayyal F. and Thach P.T. (2005). Monotonic optimization: branch and cut methods. In: Audet, C., Hansen, P., and Savard, G. (eds) Essays and Surveys on Global Optimization, pp 39--38. Springer, Berlin · Zbl 1136.90446
[18] Qu S.-J., Zhang K.-C. and Ji Y. (2007). A new global optimization algorithm for signomial geometric programming via Lagrangian relaxation. Appl. Math. Comput. 184(2): 886--894 · Zbl 1116.65071 · doi:10.1016/j.amc.2006.05.208
[19] Wang Y. and Liang Z. (2005). A deterministic global optimization algorithm for generalized geometric programming. Appl. Math. Comput. 168: 722--737 · Zbl 1105.65335 · doi:10.1016/j.amc.2005.01.142
[20] Shen P. and Jiao H. (2006). A new rectangle branch-and-pruning approach for generalized geometric programming. Appl. Math. Comput. 183: 1027--1038 · Zbl 1112.65058 · doi:10.1016/j.amc.2006.05.137
[21] Tuy H. (2005). Polynomial optimization: a robust approach. Pacific J. Optim. 1: 357--374 · Zbl 1105.90066