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モデルの 立地主体（家計と企業）の選択行動にランダム効用最大化を仮定し， FOモデルを確率的枠組み（ロジット・モデル）に拡張する． 続いて，この確率的FOモデルに対して等価最適化問題が構築できることを示す． 次に，この等価最適化問題は， 企業の立地分布を決定するマスター問題と，家計の通勤地・居住地分布を決定するサブ問題 からなる階層的最適化問題に変換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． そして，これら数理構造を活かし，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． 最後に，数値実験により提案手法の効率性・正確性を示す．
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Published: 2022-10-18 02:19:14 UTC
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Takara Sakai
Masanao Wakui
Takashi Akamatsu
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