A fast algorithm for Fujita-Ogawa model in discrete two-dimensional space
DOI:
https://doi.org/10.51094/jxiv.187Keywords:
Fujita-Ogawa (1982) model, logit model, optimal transport, Bregman's balancing method, Nesterov's accelerated gradient methodAbstract
本研究では，超大規模離散空間におけるFujita-Ogawa(FO)モデルの効率的数値解法を提案する．具体的にはまず，FOモデルにおける主体の確定的選択行動をランダム効用理論（ロジット・モデル）に基づき一般化した確率的FOモデルを提示する．続いて，この確率的FOモデルの等価最適化問題を導出し，さらにその問題が，企業の立地分布を決定するマスター問題と，家計の居住地・勤務地分布を決定するサブ問題とに階層分解できることを明らかにする．ここで，サブ問題はエントロピー正則化項付きの最適輸送問題，マスター問題は制約条件付き非凸計画問題の数理構造を持つ．これらの数理構造を活かし，サブ問題に対してはバランシング法を，マスター問題に対しては加速勾配法を適用する階層的最適化アルゴリズムを構築する．
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Submitted: 2022-10-14 08:06:33 UTC
Published: 2022-10-18 02:19:14 UTC — Updated on 2022-12-13 04:52:56 UTC
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The paper was updated with the addition of numerical experiments.License
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Takara Sakai
Masanao Wakui
Takashi Akamatsu
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