{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T16:31:47Z","timestamp":1754152307381,"version":"3.41.2"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing Municipality","doi-asserted-by":"publisher","award":["Z200002"],"award-info":[{"award-number":["Z200002"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12131003"],"award-info":[{"award-number":["12131003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p> In this paper, we propose a concept of a lattice pseudo-submodular (LPS) function and consider maximizing a monotone continuous real LPS function [Formula: see text] under a convex polytope constraint. The concept of LPS function was proposed to describe the properties of some discrete functions or nonconvex continuous functions. It is a generalization of the lattice submodular function. For the real LPS maximization problem, we design the monotone Pseudo Frank-Wolfe (PFW) algorithm by taking advantage of the second derivative bound. The PFW algorithm iterates by constantly optimize linear gradient function [Formula: see text], and finally outputs the solution. We theoretically prove that PFK algorithm has an approximation ratio of [Formula: see text] (where [Formula: see text]), and it needs at least [Formula: see text] rounds (where [Formula: see text] is a parameter given in advance). The PFW algorithm is also useful for multilinear extension of discrete lattice pseudo-submodular maximization problems. <\/jats:p>","DOI":"10.1142\/s0129054122460091","type":"journal-article","created":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T06:15:56Z","timestamp":1674195356000},"page":"731-743","source":"Crossref","is-referenced-by-count":0,"title":["Properties and Algorithm of Lattice Pseudo-Submodular Functions"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3823-4334","authenticated-orcid":false,"given":"Hongxiang","family":"Zhang","sequence":"first","affiliation":[{"name":"Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, P. R. China"}]},{"given":"Chunlin","family":"Hao","sequence":"additional","affiliation":[{"name":"Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, P. R. China"}]},{"given":"Yu","family":"Cao","sequence":"additional","affiliation":[{"name":"Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9648-7199","authenticated-orcid":false,"given":"Gaidi","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, P. R. 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