A Subgradient Method for Free Material Design
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F16%3A00507124" target="_blank" >RIV/67985556:_____/16:00507124 - isvavai.cz</a>
Result on the web
<a href="https://epubs.siam.org/doi/10.1137/15M1019660" target="_blank" >https://epubs.siam.org/doi/10.1137/15M1019660</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/15M1019660" target="_blank" >10.1137/15M1019660</a>
Alternative languages
Result language
angličtina
Original language name
A Subgradient Method for Free Material Design
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Optimization
ISSN
1052-6234
e-ISSN
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Volume of the periodical
26
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
41
Pages from-to
2314-2354
UT code for WoS article
000391853600014
EID of the result in the Scopus database
2-s2.0-85007240765