A new design optimization method is described for finding global solutions of models with a nonconvex objective function and nonlinear constraints. All functions are assumed to be generalized polynomials. By introducing new variables, the original model is transformed into one with a linear objective function, one convex and one reversed convex constraint. A two-phase algorithm that includes global feasible search and local optimal search is used for globally optimizing the transformed model. Several examples illustrate the method.
Issue Section:Research Papers
Topics:Design, Optimization, Polynomials, Algorithms
Beightler, C., and Phillips, D. T., 1976, Applied Geometric Programming, John Wiley & Sons, New York.
Dixon, L. C. W., and Szego¨, G. P., eds, 1975, Towards Global Optimization 1, Noth-Holland, Amsterdam.
Dixon, L. C. W., and Szego¨, G. P., eds, 1978, Towards Global Optimization 2, Noth-Holland, Amsterdam.
A Method for Globally Minimizing Concave Functions over Convex Sets,”
Mathematical Programming, Vol.
Optimal Design of Mechanisms Using Simulated Annealing: Theory and Applications,”
Advances in Design Automation, Rao, S. S., ed., ASME, DE-Vol.
Lo, C., 1991, “Global Optimization of Nonconvex Generalized Polynomial Design Models,” Doctoral dissertation, The University of Michigan.
McCormick, G. P., 1983, Nonlinear Programming: Theory, Algorithms and Applications, John Wiley & Sons, New York.
Papalambros, P. Y., 1988, “Remarks on Sufficiency of Constraint-bound Solutions in Optimal Design,” Advances in Design Automation-1988, S. S. Rao, ed., ASME DE-Vol. 14, New York, 1988. Also, ASME Journal of Mechanical Design in press.
Papalambros, Y. P., and Wilde, D. J., 1988, Principles of Optimal Design, Cambridge University Press, New York.
Pardalos, P. M., and Rosen, J. B., 1987, Constrained Global Optimization: Algorithms and Applications, Springer-Verlag, Berlin.
A. H. G.
Stochastic Methods for Global Optimization,”
American J. of Mathematical and Management Sciences, Vol.
1 & 2, pp.
Rockafellar, R. T., 1970, Convex Analysis, Princeton University Press, New Jersey.
Concave Programming under Linear Constraints,”
Aokl. Akad. Naul. SSSR, Vol.
A Conical Algorithm for Globally Minimizing a Concave Function over a Closed Convex Set,”
Mathematics of Operations Research, Vol.
Convex Programs with an Additional Reverse Convex Constraint,”
Journal of Optimization Theory and Applications, Vol.
Unklesbay, K., Staats, G. E., and Creighton, D. L., 1972, “Optimal Design of Pressure Vessels,” ASME Paper 72-PVP-2.
Wilde, D. J., 1978, Globally Optimal Design, John Wiley & Sons, New York.
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