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Published in:
2019 | OriginalPaper | Chapter
An Algorithm for Constrained Optimization with Applications to the Design of Mechanical Structures
Authors : Cristian Barbarosie, Sérgio Lopes, Anca-Maria Toader
Published in: EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization
Publisher: Springer International Publishing
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Abstract
We propose an algorithm for minimizing a functional under constraints. It uses first 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 involves 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 satisfied in the limit (after convergence). Although the algorithm can be used as a general-purpose optimization tool, it is designed specifically for problems where first order derivatives of both objective and constraint functionals are available but not second order derivatives (as is often the case in structural optimization).