## Abstract

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.

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.

Original language | English |
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Journal | S I A M Journal on Optimization |

Volume | 10 |

Issue number | 4 |

Pages (from-to) | 982-998 |

ISSN | 1052-6234 |

DOIs | |

Publication status | Published - 18 Jun 2000 |

## Keywords

- nonlinear optimization
- structural optimization
- variational methods