Journal article
An Optimization Problem for Predicting the Maximal Effect of Degradation of Mechanical Structures
This paper deals with a nonlinear nonconvex optimization problem that models prediction of degradation in discrete or discretized mechanical structures. The mathematical difficulty lies in equality constraints of the form Σ(i=1)(m) 1/yi A(i) x=b, where A(i) are symmetric and positive semidefinite matrices, b is a vector, and x, y are the vectors of unknowns.
The linear objective function to be maximized is (x, y) bar right arrow b(T)x. In a first step we investigate the problem properties such as existence of solutions and the differentiability of related marginal functions. As a by-product, this gives insight in terms of a mechanical interpretation of the optimization problem.
We derive an equivalent convex problem formulation and a convex dual problem, and for dyadic matrices A(i) a quadratic programming problem formulation is developed. A nontrivial numerical example is included, based on the latter formulation.
Language: | English |
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Year: | 2000 |
Pages: | 982-998 |
ISSN: | 10957189 and 10526234 |
Types: | Journal article |
DOI: | 10.1137/S1052623497328768 |
ORCIDs: | Bendsøe, Martin P. |