{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:50:15Z","timestamp":1760151015800,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T00:00:00Z","timestamp":1643068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873254"],"award-info":[{"award-number":["61873254"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we propose a parallel algorithm for a fund of fund (FOF) optimization model. Based on the structure of objective function, we create an augmented Lagrangian function and separate the quadratic term from the nonlinear term by the alternate direction multiplier method (ADMM), which creates two new subproblems that are much easier to be computed. To accelerate the convergence speed of the proposed algorithm, we use an adaptive step size method to adjust the step parameter according to the residual of the dual problem at every iterate. We show the parallelization of the proposed algorithm and implement it on CUDA with block storage for the structured matrix, which is shown to be up to two orders of magnitude faster than the CPU implementation on large-scale problems.<\/jats:p>","DOI":"10.3390\/a15020035","type":"journal-article","created":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T20:44:33Z","timestamp":1643143473000},"page":"35","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An ADMM Based Parallel Approach for Fund of Fund Construction"],"prefix":"10.3390","volume":"15","author":[{"given":"Yidong","family":"Chen","sequence":"first","affiliation":[{"name":"Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7244-3458","authenticated-orcid":false,"given":"Chen","family":"Li","sequence":"additional","affiliation":[{"name":"Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"Zhonghua","family":"Lu","sequence":"additional","affiliation":[{"name":"Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1080\/09603100600970099","article-title":"The performance evaluation for fund of funds by comparing asset allocation of mean\u2013variance model or genetic algorithms to that of fund managers","volume":"18","author":"Lai","year":"2008","journal-title":"Appl. Financ. Econ."},{"key":"ref_2","first-page":"77","article-title":"Portfolio Selection","volume":"7","author":"Markowitz","year":"1952","journal-title":"J. Financ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1093\/rfs\/4.2.315","article-title":"On the sensitivity of mean-variance-efficient portfolios to changes in asset means: Some analytical and computational results","volume":"4","author":"Best","year":"1991","journal-title":"Rev. Financ. Stud."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF02282040","article-title":"Computing efficient frontiers using estimated parameters","volume":"45","author":"Broadie","year":"1993","journal-title":"Ann. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1287\/mnsc.37.5.519","article-title":"Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market","volume":"37","author":"Konno","year":"1991","journal-title":"Manag. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1111\/1467-9965.00068","article-title":"Coherent measures of risk","volume":"9","author":"Artzner","year":"1999","journal-title":"Math. Financ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"21","DOI":"10.21314\/JOR.2000.038","article-title":"Optimization of conditional value-at-risk","volume":"2","author":"Rockafellar","year":"2000","journal-title":"J. Risk"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chekhlov, A., Uryasev, S., and Zabarankin, M. (2004). Portfolio optimization with drawdown constraints. Supply Chain and Finance, World Scientific.","DOI":"10.1142\/9789812562586_0013"},{"key":"ref_9","first-page":"1","article-title":"Global asset allocation with equities, bonds, and currencies","volume":"2","author":"Black","year":"1991","journal-title":"Fixed Income Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"28","DOI":"10.2469\/faj.v48.n5.28","article-title":"Global portfolio optimization","volume":"48","author":"Black","year":"1992","journal-title":"Financ. Anal. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"47","DOI":"10.2469\/faj.v68.n1.1","article-title":"Leverage aversion and risk parity","volume":"68","author":"Asness","year":"2012","journal-title":"Financ. Anal. J."},{"key":"ref_12","unstructured":"Nemirovskii, A.S., and Nesterov, Y.E. (1994). Interior-point polynomial algorithms in convex programming. Stud. Appl. Math. Phila. Siam."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1137\/0805002","article-title":"Interior point method in semidefinite programming with application to combinatorial optimization","volume":"5","author":"Alizadeh","year":"1995","journal-title":"Siam J. Optim."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/PL00011391","article-title":"A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming","volume":"89","author":"Byrd","year":"2000","journal-title":"Math. Program."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1155\/2013\/295147","article-title":"Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique","volume":"2013","author":"Han","year":"2013","journal-title":"J. Appl. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s10589-015-9820-y","article-title":"An inertia-free filter line-search algorithm for large-scale nonlinear programming","volume":"64","author":"Chiang","year":"2016","journal-title":"Comput. Optim. Appl."},{"key":"ref_17","unstructured":"Hult, H., Lindskog, F., Hammarlid, O., and Rehn, C.J. (2012). Springer Series in Operations Research and Financial Engineering, Springer."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0045-7825(77)90049-4","article-title":"Numerical solution of two-dimensional magnetostatic problems by augmented lagrangian methods","volume":"12","author":"Glowinski","year":"1977","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chaves, D.B., Hsu, J.C., Li, F., and Shakernia, O. (2011). Risk Parity Portfolio vs. Other Asset Allocation Heuristic Portfolios. Soc. Sci. Electron. Publ., 20.","DOI":"10.3905\/joi.2011.20.1.108"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1080\/14697688.2015.1031815","article-title":"Least-squares approach to risk parity in portfolio selection","volume":"16","author":"Bai","year":"2016","journal-title":"Quant. Financ."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Costa, G., and Kwon, R.H. (2020). Generalized risk parity portfolio optimization: An ADMM approach. J. Glob. Optim.","DOI":"10.2139\/ssrn.3609374"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s12532-015-0078-2","article-title":"Generalized Alternating Direction Method of Multipliers: New Theoretical Insights and Applications","volume":"7","author":"Fang","year":"2015","journal-title":"Math. Program. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1137\/110836936","article-title":"On the O(1\/n) Convergence Rate of the Douglas-Rachford Alternating Direction Method","volume":"50","author":"He","year":"2012","journal-title":"Siam J. Numer. Anal."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Banjac, G., Goulart, P., Stellato, B., and Boyd, S. (2018, January 5\u20137). Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization. Proceedings of the 2018 UKACC 12th International Conference on Control (CONTROL), Sheffield, UK.","DOI":"10.1109\/CONTROL.2018.8516858"},{"key":"ref_25","unstructured":"Xu, Z., Figueiredo, M.A.T., and Goldstein, T. (2016). Adaptive ADMM with Spectral Penalty Parameter Selection. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Stellato, B., Banjac, G., Goulart, P., Bemporad, A., and Boyd, S. (2018, January 5\u20137). OSQP: An Operator Splitting Solver for Quadratic Programs. Proceedings of the 2018 UKACC 12th International Conference on Control (CONTROL), Sheffield, UK.","DOI":"10.1109\/CONTROL.2018.8516834"},{"key":"ref_27","unstructured":"Kirk, D.B., and Wen, M. (2016). Programming Massively Parallel Processors: A Hands-on Approach, Morgan Kaufmann. [3rd ed.]."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/2\/35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:07:19Z","timestamp":1760134039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/2\/35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,25]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["a15020035"],"URL":"https:\/\/doi.org\/10.3390\/a15020035","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,1,25]]}}}