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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Sequential Explicit, Convex Approximations
verfasst von : Peter W. Christensen, Anders Klarbring
Erschienen in: An Introduction to Structural Optimization
Verlag: Springer Netherlands
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In the previous two chapters we were able to formulate a number of structural optimization problems where both the objective function and all of the constraints were written as explicit functions of the design variables only. For larger problems, however, it is in general practically impossible to obtain such explicit functions. Our remedy to be able to solve large-scale problems is to generate a sequence of explicit subproblems that are approximations of the original problem and solve these subproblems instead.
As already mentioned, most problems in structural optimization are nonconvex. Because of the intrinsic difficulties with solving nonconvex problems, we will choose approximations that are convex. In this chapter, a number of explicit, convex approximations will be described. The main focus will be on approximations that take into account specific characteristics of certain structural optimization problems.