{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T19:36:18Z","timestamp":1754163378127,"version":"3.41.2"},"reference-count":35,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12271015"],"award-info":[{"award-number":["12271015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Hong Kong Research Grant Council under Project GRF","award":["15307822"],"award-info":[{"award-number":["15307822"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12271015"],"award-info":[{"award-number":["12271015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p> Harmonic model predictive control (HMPC) is a variant of MPC that offers improved system performance compared to other MPC formulations within a shorter prediction horizon. However, achieving this benefit requires formulating the MPC as a quadratic second-order cone programming (QSOCP) problem, as opposed to the conventional quadratic programming problem commonly found in linear MPC formulations. This distinction arises from the need to incorporate a special class of second-order cone (SOC) intersections in the constraints. To handle the cone constraints in this problem efficiently, we introduced an explicit expression for the intersection of the SOC constraints and derived a closed-form solution projected onto it. By exploiting the inherent sparsity structure of the HMPC problem and using Cholesky decomposition, we reformulate it as a strongly QSOCP problem. This reformulation allows us to represent the objective function as a quadratic function using an identity matrix. We then use the Halpern fixed-point iteration-based scheme to solve this problem. Through numerical experiments, we demonstrated the superiority of our proposed method in terms of the computational time required to solve HMPC problems. <\/jats:p>","DOI":"10.1142\/s0217595924500283","type":"journal-article","created":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T11:43:02Z","timestamp":1728646982000},"source":"Crossref","is-referenced-by-count":0,"title":["A Halpern Fixed-Point Iteration-Based Approach to Harmonic Model Predictive Control Problem"],"prefix":"10.1142","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3903-5673","authenticated-orcid":false,"given":"Bo","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. 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