Semi-supervised clustering problems focus on clustering data with labels. In this paper,we consider the semi-supervised hypergraph problems. We use the hypergraph related tensor to construct an orthogonal constrained optimization model. The optimization problem is solved by a retraction method, which employs the polar decomposition to map the gradient direction in the tangent space to the Stefiel manifold. A nonmonotone curvilinear search is implemented to guarantee reduction in the objective function value. Convergence analysis demonstrates that the first order optimality condition is satisfied at the accumulation point. Experiments on synthetic hypergraph and hypergraph given by real data demonstrate the effectivity of our method.
{"title":"A gradient projection method for semi-supervised hypergraph clustering problems","authors":"Jingya Chang, Dongdong Liu, Min Xi","doi":"10.61208/pjo-2023-025","DOIUrl":"https://doi.org/10.61208/pjo-2023-025","url":null,"abstract":"Semi-supervised clustering problems focus on clustering data with labels. In this paper,we consider the semi-supervised hypergraph problems. We use the hypergraph related tensor to construct an orthogonal constrained optimization model. The optimization problem is solved by a retraction method, which employs the polar decomposition to map the gradient direction in the tangent space to the Stefiel manifold. A nonmonotone curvilinear search is implemented to guarantee reduction in the objective function value. Convergence analysis demonstrates that the first order optimality condition is satisfied at the accumulation point. Experiments on synthetic hypergraph and hypergraph given by real data demonstrate the effectivity of our method.","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43706187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we discuss variational inequality (VI) problems without monotonicity from the perspective of convergence of projection-type algorithms. In particular, we identify existing conditions as well as present new conditions that are sufficient to guarantee convergence. The first half of the paper focuses on the case where a Minty solution exists (also known as Minty condition), which is a common assumption in the recent developments for non-monotone VI. The second half explores alternative sufficient conditions that are different from the existing ones such as monotonicity or Minty condition, using an algorithm-based approach. Through examples and convergence analysis, we show that these conditions are capable of characterizing different classes of VI problems where the algorithms are guaranteed to converge.
{"title":"Beyond Monotone Variational Inequalities: Solution Methods and Iteration Complexities","authors":"Kevin Huang, Shuzhong Zhang","doi":"10.61208/pjo-2023-021","DOIUrl":"https://doi.org/10.61208/pjo-2023-021","url":null,"abstract":"In this paper, we discuss variational inequality (VI) problems without monotonicity from the perspective of convergence of projection-type algorithms. In particular, we identify existing conditions as well as present new conditions that are sufficient to guarantee convergence. The first half of the paper focuses on the case where a Minty solution exists (also known as Minty condition), which is a common assumption in the recent developments for non-monotone VI. The second half explores alternative sufficient conditions that are different from the existing ones such as monotonicity or Minty condition, using an algorithm-based approach. Through examples and convergence analysis, we show that these conditions are capable of characterizing different classes of VI problems where the algorithms are guaranteed to converge.","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43116869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A self-adaptive inertial viscosity projection algorithm for solving split feasibility problem with multiple output sets","authors":"Y. Dang, Caihua Hou, Liu Yang","doi":"10.61208/pjo-2023-002","DOIUrl":"https://doi.org/10.61208/pjo-2023-002","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"8 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71278518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Long Abstract of Manuscript for Pacific Journal of Optimization","authors":"WANG Fenlan","doi":"10.61208/pjo-2023-031","DOIUrl":"https://doi.org/10.61208/pjo-2023-031","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135103266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the D-gap functions for variational-hemivariational inequalities with an application to contact mechanics","authors":"Tam Vo Minh, Chen Jein-Shan","doi":"10.61208/pjo-2023-033","DOIUrl":"https://doi.org/10.61208/pjo-2023-033","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135158585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Research on Optimality Conditions for SSOCCVI Problem","authors":"Wang Li, Mengdi Zheng, Sun Juhe, Liu Hao","doi":"10.61208/pjo-2023-005","DOIUrl":"https://doi.org/10.61208/pjo-2023-005","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71278585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The hypertree with the second largest spectral radius among uniform hypertrees with given size and stability number","authors":"SURFACESWei-ping Li, Honghai Li","doi":"10.61208/pjo-2023-018","DOIUrl":"https://doi.org/10.61208/pjo-2023-018","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71278413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Penalty-based Method for Solving a Discrete HJB Complementarity Problem","authors":"Zhang K., Yang X., W. S.","doi":"10.61208/pjo-2023-011","DOIUrl":"https://doi.org/10.61208/pjo-2023-011","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71278671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mean-variance analysis of sustainable newsvendor problems with stochastic demand under cap-and-trade policy","authors":"Bai Qingguo, Lu Hongling, Meng Fanwen","doi":"10.61208/pjo-2023-029","DOIUrl":"https://doi.org/10.61208/pjo-2023-029","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"240 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136304480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new three-term conjugate gradient method with adaptively alternative two-side approximating strategy that generates descent search direction","authors":"Dong Xiaoliang, Han Deren","doi":"10.61208/pjo-2023-028","DOIUrl":"https://doi.org/10.61208/pjo-2023-028","url":null,"abstract":"","PeriodicalId":49716,"journal":{"name":"Pacific Journal of Optimization","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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