Browsing by Author "Toader, Anca-Maria"
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- An algorithm for constrained optimization with applications to the design of mechanical structuresPublication . Barbarosie, Cristian; Lopes, Sérgio; Toader, Anca-MariaWe 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).
- A gradient-type algorithm for constrained optimization with application to microstructure optimizationPublication . Barbarosie, Cristian; Toader, Anca-Maria; Lopes, S.We propose a method to optimize periodic microstructures for obtaining homogenized materials with negative Poisson ratio, using shape and/or topology variations in the model hole. The proposed approach employs worst case design in order to minimize the Poisson ratio of the (possibly anisotropic) homogenized elastic tensor in several prescribed directions. We use a minimization algorithm for inequality constraints based on an active set strategy and on a new algorithm for solving minimization problems with equality constraints, belonging to the class of null-space gradient methods. 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 (minimizing the objective functional) and a correction step related to the Newton method (aiming 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). A local convergence result is proven for a general nonlinear setting, where both the objective functional and the constraints are not necessarily convex functions.