Počet záznamů: 1
A Subgradient Method for Free Material Design
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SYSNO ASEP 0507124 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název A Subgradient Method for Free Material Design Tvůrce(i) Kočvara, Michal (UTIA-B) RID, ORCID
Xia, Y. (CA)
Nesterov, Y. (BE)Celkový počet autorů 3 Zdroj.dok. SIAM Journal on Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1052-6234
Roč. 26, č. 4 (2016), s. 2314-2354Poč.str. 41 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova fast gradient method ; Nesterov’s primal-dual subgradient method ; free material optimization Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Způsob publikování Open access Institucionální podpora UTIA-B - RVO:67985556 UT WOS 000391853600014 EID SCOPUS 85007240765 DOI 10.1137/15M1019660 Anotace 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.
Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2020 Elektronická adresa https://epubs.siam.org/doi/10.1137/15M1019660
Počet záznamů: 1