Primal and Dual Methods in Structural Optimization

by C. Fleury, Postdoctoral Research Fellow; Univ. of California, Los Angeles, Calif.; Aspirant du Fonds National Belge de la Recherche Scientifique,
Lucien A. Schmit, (F.ASCE), Prof. of Engrg. and Applied Sci.; Univ. of California, Los Angeles, Calif.,

Serial Information: Journal of the Structural Division, 1980, Vol. 106, Issue 5, Pg. 1117-1133

Document Type: Journal Paper


The most natural way of attacking a structural optimization problem is to make use of mathematical programming methods. This approach has gradually evolved into a powerful design scheme that proceeds by linearizing the potentially active constraints with respect to the reciprocal design variables and solving partially the resulting explicit problem before reanalyzing the structure and updating the approximate problem statement. This approach can be viewed as a primal method since the goal is to generate a sequence of feasible designs with decreasing weight. An alternative approach is to recognize that the expliit but approximate problem statement is of such high quality that it can be solved exactly after each structural reanalysis. Adopting this viewpoint leads naturally to consideration of dual methods for solving the explicit problem. This approach can be interpreted as a rigorous generalization of the conventional optimality criteria techniques.

Subject Headings: Optimization models | Computer programming | Linear functions

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