An algorithm for constrained optimization with applications to the design of mechanical structures
We propose an algorithm for minimizing a functional under constraints. It uses _rst order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest descent step (which minimizes the objective functional) and a correction step related to the Newt...
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| Other Authors: | , |
| Format: | conferenceObject |
| Language: | eng |
| Published: |
2018
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10400.21/8914 |
| Country: | Portugal |
| Oai: | oai:repositorio.ipl.pt:10400.21/8914 |
| Summary: | We propose an algorithm for minimizing a functional under constraints. It uses _rst order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest descent step (which minimizes the objective functional) and a correction step related to the Newton method (which aims to solve the equality constraints). The linear combination between these two steps envolves coefficients similar to Lagrange multipliers which are computed in a natural way based on the Newton method. The algorithm uses no projection and thus the iterates are not feasible; the constraints are only satis_ed in the limit (after convergence). Although the algorithm can be used as a general-purpose optimization tool, it is designed speci_cally for problems where _rst order derivatives of both objective and constraint functionals are available but not second order derivatives (as is often the case in structural optimization). |
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