Document type
Journal articles
Document subtype
Full paper
Title
A gradient-type algorithm for constrained optimization with application to microstructure optimization
Participants in the publication
Cristian Barbarosie (Author)
Dep. Matemática
CMAFcIO
Anca-Maria Toader (Author)
Dep. Matemática
CMAFcIO
Sérgio Lopes (Author)
CMAFcIO
Summary
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.
Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA
Where published
Discrete & Continuous Dynamical Systems - B
Publication Identifiers
ISSN - 1553-524X
Publisher
American Institute of Mathematical Sciences (AIMS)
Number of pages
26
Starting page
1729
Last page
1755
Document Identifiers
DOI -
https://doi.org/10.3934/dcdsb.2019249
URL -
http://dx.doi.org/10.3934/dcdsb.2019249
Rankings
SCOPUS Q3 (2019) - 1.7 - Applied Mathematics
SCOPUS Q2 (2019) - 1.7 - Discrete Mathematics and Combinatorics
SCIMAGO Q1 (2019) - 0.816 - Applied Mathematics (Q2)
SCIMAGO Q1 (2019) - 0.816 - Discrete Mathematics and Combinatorics
Keywords
nonlinear programming
constrained minimization
worst case design
optimization of microstructures
porous materials
microstructure
auxetic materials