@article{oai:nagoya.repo.nii.ac.jp:00019099,
 author = {畔上, 秀幸 and Azegami, Hideyuki},
 issue = {2},
 journal = {日本応用数理学会論文誌},
 month = {Jun},
 note = {形状最適化問題は偏微分方程式の境界値問題が定義された領域の境界形状に対する最適化問題として定義される.設計変数は領域写像で与えられる.評価関数は設計変数と境界値問題の解に対する汎関数で与えられる.本論文では,評価関数の領域変動に対するFrechet微分は次の領域を定義できる正則性を備えていないこと,およびその微分を正則化する関数空間の勾配法が考えられることを示した., A shape optimization problem is defined as an optimization problem to boundary shape of domain in which boundary value problem of partial differential equation is defined. A design variable is given by a domain mapping. Cost functions are defined as functionals of the design variable and the solution to the boundary value problem. The present paper described that the Frechet derivatives of cost functions with respect to domain variation do not have the regularity required in order to define a next domain, and that a gradient method can be considered for regularizing the derivatives.},
 pages = {83--137},
 title = {形式最適化問題の正則化解法},
 volume = {24},
 year = {2014}
}