| bibtype |
J -
Journal Article
|
| ARLID |
0507124 |
| utime |
20240103222343.6 |
| mtime |
20190731235959.9 |
| SCOPUS |
85007240765 |
| WOS |
000391853600014 |
| DOI |
10.1137/15M1019660 |
| title
(primary) (eng) |
A Subgradient Method for Free Material Design |
| specification |
| page_count |
41 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0255073 |
| ISSN |
1052-6234 |
| title
|
SIAM Journal on Optimization |
| volume_id |
26 |
| volume |
4 (2016) |
| page_num |
2314-2354 |
| publisher |
| name |
SIAM Society for Industrial and Applied Mathematics |
|
|
| keyword |
fast gradient method |
| keyword |
Nesterov’s primal-dual subgradient method |
| keyword |
free material optimization |
| author
(primary) |
| ARLID |
cav_un_auth*0101131 |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept (eng) |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department (eng) |
MTR |
| full_dept |
Department of Decision Making Theory |
| share |
33 |
| name1 |
Kočvara |
| name2 |
Michal |
| institution |
UTIA-B |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0377831 |
| share |
34 |
| name1 |
Xia |
| name2 |
Y. |
| country |
CA |
|
| author
|
| ARLID |
cav_un_auth*0377832 |
| share |
33 |
| name1 |
Nesterov |
| name2 |
Y. |
| country |
BE |
|
| source |
|
| source |
|
| cas_special |
| abstract
(eng) |
A small improvement in the structure of the material could save the manufactory a lot of money. The free material design can be formulated as an optimization problem. However, due to its large scale, second order methods cannot solve the free material design problem in reasonable size. We formulate the free material optimization (FMO) problem into a saddle-point form in which the inverse of the stiffness matrix A(E) in the constraint is eliminated. The size of A(E) is generally large, denoted as N × N. We apply the primal-dual subgradient method to solve the restricted saddle-point formula. This is the first gradient-type method for FMO. Each iteration of our algorithm takes a total of O(N^2) floating-point operations and an auxiliary vector storage of size O(N), compared with formulations having the inverse of A(E) which requires O(N^3) arithmetic operations and an auxiliary vector storage of size O(N^2). To solve the problem, we developed a closed-form solution to a semidefinite least squares problem and an efficient parameter update scheme for the gradient method, which are included in the appendix. We also approximate a solution to the bounded Lagrangian dual problem. The problem is decomposed into small problems each only having an unknown of k × k (k = 3 or 6) matrix, and can be solved in parallel. The iteration bound of our algorithm is optimal for general subgradient scheme. Finally we present promising numerical results.\n |
| result_subspec |
WOS |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10101 |
| reportyear |
2020 |
| num_of_auth |
3 |
| inst_support |
RVO:67985556 |
| permalink |
http://hdl.handle.net/11104/0298529 |
| confidential |
S |
| mrcbC86 |
3+4 Article Mathematics Applied |
| mrcbC91 |
A |
| mrcbT16-e |
MATHEMATICSAPPLIED |
| mrcbT16-j |
2.759 |
| mrcbT16-s |
2.652 |
| mrcbT16-4 |
Q1 |
| mrcbT16-B |
98.129 |
| mrcbT16-D |
Q1* |
| mrcbT16-E |
Q1* |
| arlyear |
2016 |
| mrcbU14 |
85007240765 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
000391853600014 WOS |
| mrcbU63 |
cav_un_epca*0255073 SIAM Journal on Optimization 1052-6234 1095-7189 Roč. 26 č. 4 2016 2314 2354 SIAM Society for Industrial and Applied Mathematics |
|