Solving policy design problems: Alternating direction method of multipliers-based methods for structured inverse variational inequalities |
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| Institution: | 1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China;2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China;3. School of Mathematics and Systems Science, Beijing Advanced Innovation Center for Big Data and Brain Computing (BDBC), Beihang University, Beijing 100191, PR China;1. School of Economic Mathematics and Collaborative Innovation Center of Financial Security, Southwestern University of Finance and Economics, Chengdu 611130, China;2. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China;3. Department of Mathematics, Imperial College, London SW7 2BZ, UK;1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia;1. Department of Logistics Management, School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China;2. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Special Administrative Region;1. Department of Economics, Oregon State University, Corvallis, OR, USA;2. Department of Applied Economics, University of Maryland, College Park, MD, USA;3. Department of Economics, Southern Illinois University, Carbondale, IL, USA;4. Department of Accounting, Economics and Finance, Southeast Missouri State University, Cape Girardeau, MO, USA;1. Department of Mathematics, Technische Universität Kaiserslautern, Germany;2. School of Mathematics and Natural Sciences, University of Wuppertal, Germany;3. Department of Mathematical Sciences, Clemson University, SC, USA |
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| Abstract: | Inverse variational inequalities have broad applications in various disciplines, and some of them have very appealing structures. There are several algorithms (e.g., proximal point algorithms and projection-type algorithms) for solving the inverse variational inequalities in general settings, while few of them have fully exploited the special structures. In this paper, we consider a class of inverse variational inequalities that has a separable structure and linear constraints, which has its root in spatial economic equilibrium problems. To design an efficient algorithm, we develop an alternating direction method of multipliers (ADMM) based method by utilizing the separable structure. Under some mild assumptions, we prove its global convergence. We propose an improved variant that makes the subproblems much easier and derive the convergence result under the same conditions. Finally, we present the preliminary numerical results to show the capability and efficiency of the proposed methods. |
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