Distributed Fixed Point Subgradient Methods for Solving Large-scale, Complicated Network Resource Allocation Problems

• Project/Area Number: 15K04763
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computational science
• Research Institution: Meiji University
• Principal Investigator: IIDUKA HIDEAKI 明治大学, 理工学部, 専任准教授 (50532280)
• Research Collaborator: HISHINUMA Kazuhiro
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: ネットワーク資源割り当て / 分散最適化 / 不動点 / 凸最適化 / 非拡大写像

Outline of Final Research Achievements

We formulated large-scale, complicated network resource allocation problems as a distributed optimization problem over fixed point sets of nonexpansive mappings and devised acceleration methods for solving the problem. We showed that the methods converge to a solution to the problem under certain assumptions. We numerically compared the proposed methods with the conventional ones. The numerical experiments demonstrated the effectiveness and optimality of the proposed methods.

Research Products

• [Journal Article] Two stochastic optimization algorithms for convex optimization with fixed point constraints (2018)
  • Author(s): Hideaki Iiduka
  • Journal Title: Optimization Methods and Software Volume: 印刷中 Issue: 4 Pages: 731-757
  • DOI: 10.1080/10556788.2018.1425860
  • Peer Reviewed
• [Journal Article] Evaluation of stochastic approximation algorithm and variants for learning support vector machines (2018)
  • Author(s): Keigo Fujiwara, Kazuhiro Hishinuma, and Hideaki Iiduka
  • Journal Title: Linear and Nonlinear Analysis Volume: 4 Pages: 29-61
  • Peer Reviewed / Open Access
• [Journal Article] Optimality and convergence for convex ensemble learning with sparsity and diversity based on fixed point optimization (2018)
  • Author(s): Yoichi Hayashi and Hideaki Iiduka
  • Journal Title: Neurocomputing Volume: 273 Pages: 367-372
  • DOI: 10.1016/j.neucom.2017.07.046
  • Peer Reviewed
• [Journal Article] 不動点制約付き非平滑凸最適化 (2018)
  • Author(s): 飯塚 秀明
  • Journal Title: オペレーションズ・リサーチ 経営の科学-特集 第29回RAMPシンポジウム Volume: 63 Pages: 153-159
  • Open Access
• [Journal Article] Convergence rate analysis of projected stochastic subgradient method using conjugate gradient-like direction (2017)
  • Author(s): Yuta Sekine and Hideaki Iiduka
  • Journal Title: Linear and Nonlinear Analysis Volume: 3 Pages: 203-211
  • Peer Reviewed / Open Access
• [Journal Article] Almost sure convergence of random projected proximal and subgradient algorithms for distributed nonsmooth convex optimization (2017)
  • Author(s): Hideaki Iiduka
  • Journal Title: Optimization Volume: 66 Issue: 1 Pages: 35-59
  • DOI: 10.1080/02331934.2016.1252914
  • Peer Reviewed
• [Journal Article] 不動点制約付き非平滑凸最適化とその応用 (2017)
  • Author(s): 飯塚 秀明
  • Journal Title: 日本オペレーションズ・リサーチ学会 数理計画研究部会 第29回RAMPシンポジウム論文集 Volume: - Pages: 125-142
• [Journal Article] Convergence Analysis of Iterative Methods for Nonsmooth Convex Optimization over Fixed Point Sets of Quasi-Nonexpansive Mappings (2016)
  • Author(s): Hideaki Iiduka
  • Journal Title: Mathematical Programming Volume: 159 Issue: 1-2 Pages: 509538-509538
  • DOI: 10.1007/s10107-015-0967-1
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Incremental Subgradient Method for Nonsmooth Convex Optimization with Fixed Point Constraints (2016)
  • Author(s): Hideaki Iiduka
  • Journal Title: Optimization Methods and Software Volume: 31 Issue: 5 Pages: 931951-931951
  • DOI: 10.1080/10556788.2016.1175002
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Line Search Fixed Point Algorithms Based on Nonlinear Conjugate Gradient Directions: Application to Constrained Smooth Convex Optimization (2016)
  • Author(s): Hideaki Iiduka
  • Journal Title: Fixed Point Theory and Applications Volume: 2016 Issue: 1 Pages: 77-77
  • DOI: 10.1186/s13663-016-0567-7
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Proximal Point Algorithms for Nonsmooth Convex Optimization with Fixed Point Constraints (2016)
  • Author(s): Hideaki Iiduka
  • Journal Title: European Journal of Operational Research Volume: 253 Issue: 2 Pages: 503513-503513
  • DOI: 10.1016/j.ejor.2016.02.057
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimization for Inconsistent Split Feasibility Problems (2016)
  • Author(s): Hideaki Iiduka
  • Journal Title: Numerical Functional Analysis and Optimization Volume: 37 Issue: 2 Pages: 186205-186205
  • DOI: 10.1080/01630563.2015.1080270
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Distributed Convex Optimization Algorithms and Their Application to Distributed Control in Peer-to-Peer Data Storage System (2015)
  • Author(s): Hideaki Iiduka
  • Journal Title: Journal of Nonlinear and Convex Analysis Volume: 16 Pages: 21592179-21592179
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Parallel Optimization Algorithm for Smooth Convex Optimization over Fixed Point Sets of Quasi-Nonexpansive Mappings (2015)
  • Author(s): Hideaki Iiduka
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 58 Pages: 330352-330352
  • NAID: 130005108558
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Parallel Subgradient Method for Nonsmooth Convex Optimization with a Simple Constraint (2015)
  • Author(s): Kazuhiro Hishinuma, Hideaki Iiduka
  • Journal Title: Linear and Nonlinear Analysis Volume: 1 Pages: 6777-6777
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Parallel Computing Subgradient Method for Nonsmooth Convex Optimization over the Intersection of Fixed Point Sets of Nonexpansive Mappings (2015)
  • Author(s): Hideaki Iiduka
  • Journal Title: Fixed Point Theory and Applications Volume: 72 Issue: 1 Pages: 117-117
  • DOI: 10.1186/s13663-015-0319-0
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Convex Optimization over Fixed Point Sets of Quasi-Nonexpansive and Nonexpansive Mappings in Utility-Based Bandwidth Allocation Problems with Operational Constraints (2015)
  • Author(s): Hideaki Iiduka
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 282 Pages: 225236-225236
  • DOI: 10.1016/j.cam.2014.12.048
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] 不動点制約付き非平滑凸最適化とその応用 (2017)
  • Author(s): 飯塚 秀明
  • Organizer: 日本オペレーションズ・リサーチ学会 数理計画研究部会 第29回RAMPシンポジウム
  • Invited
• [Remarks] 数理最適化研究室へようこそ
  • URL: http://www.mo.cs.meiji.ac.jp/