Pub Date : 2023-11-01DOI: 10.4208/jcm.2303-m2021-0309
Sihong Shao, Dong Zhang and Weixi Zhang null
We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and the best known ones are at least $0.986$ and can be further improved to at least $0.997$ by a preliminary attempt to break out of local optima.
{"title":"A Simple Iterative Algorithm for Maxcut","authors":"Sihong Shao, Dong Zhang and Weixi Zhang null","doi":"10.4208/jcm.2303-m2021-0309","DOIUrl":"https://doi.org/10.4208/jcm.2303-m2021-0309","url":null,"abstract":"We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and the best known ones are at least $0.986$ and can be further improved to at least $0.997$ by a preliminary attempt to break out of local optima.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"238 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135217556","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}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2305-m2022-0268
Jie Xu and Mingbo Zhang
{"title":"Wong-Zakai Approximations for Stochastic Volterra Equations","authors":"Jie Xu and Mingbo Zhang","doi":"10.4208/jcm.2305-m2022-0268","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2022-0268","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139299758","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}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2305-m2023-0014
Daxin Nie and Weihua Deng
{"title":"Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven By Fractional Gaussian Noise","authors":"Daxin Nie and Weihua Deng","doi":"10.4208/jcm.2305-m2023-0014","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2023-0014","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"131 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139305528","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}
Pub Date : 2023-10-01DOI: 10.4208/jcm.2301-m2022-0088
Jingjun Zhao, Hao Zhou and Yang Xu
{"title":"Modified Split-Step Theta Method for Stochastic Differential Equations Driven By Fractional Brownian Motion","authors":"Jingjun Zhao, Hao Zhou and Yang Xu","doi":"10.4208/jcm.2301-m2022-0088","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2022-0088","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135706056","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}
Pub Date : 2023-10-01DOI: 10.4208/jcm.2307-m2021-0331
Nachuan Xiao and Xin Liu
In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, ExPen adopts a smooth penalty function without using any first-order derivative of the objective function. We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible, namely, are the first-order stationary points of the original optimization problem, or far from the Stiefel manifold. Besides, the original problem and ExPen share the same second-order stationary points. Remarkably, the exact gradient and Hessian of ExPen are easy to compute. As a consequence, abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.
{"title":"Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Functions","authors":"Nachuan Xiao and Xin Liu","doi":"10.4208/jcm.2307-m2021-0331","DOIUrl":"https://doi.org/10.4208/jcm.2307-m2021-0331","url":null,"abstract":"In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, ExPen adopts a smooth penalty function without using any first-order derivative of the objective function. We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible, namely, are the first-order stationary points of the original optimization problem, or far from the Stiefel manifold. Besides, the original problem and ExPen share the same second-order stationary points. Remarkably, the exact gradient and Hessian of ExPen are easy to compute. As a consequence, abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"2011 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136094371","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}
Pub Date : 2023-10-01DOI: 10.4208/jcm.2301-m2022-0116
Mengyun Wang, Ye Ji and Chungang Zhu
{"title":"Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis","authors":"Mengyun Wang, Ye Ji and Chungang Zhu","doi":"10.4208/jcm.2301-m2022-0116","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2022-0116","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135706411","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}
Pub Date : 2023-10-01DOI: 10.4208/jcm.2301-m2022-0065
Pierluigi Amodio, Luigi Brugnano, Gianluca Frasca-Caccia and Felice Iavernaro
In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within the so-called line integral framework. Numerical tests to illustrate the theoretical findings are presented.
{"title":"Arbitrarily High-Order Energy-Conserving Methods for Hamiltonian Problems with Quadratic Holonomic Constraints","authors":"Pierluigi Amodio, Luigi Brugnano, Gianluca Frasca-Caccia and Felice Iavernaro","doi":"10.4208/jcm.2301-m2022-0065","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2022-0065","url":null,"abstract":"In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within the so-called line integral framework. Numerical tests to illustrate the theoretical findings are presented.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135705863","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}
Pub Date : 2023-10-01DOI: 10.4208/jcm.2309-m2023-0041
Duo Qiu, Michael K. Ng and Xiongjun Zhang
{"title":"Low-Rank Matrix Completion with Poisson Observations via Nuclear Norm and Total Variation Constraints","authors":"Duo Qiu, Michael K. Ng and Xiongjun Zhang","doi":"10.4208/jcm.2309-m2023-0041","DOIUrl":"https://doi.org/10.4208/jcm.2309-m2023-0041","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135922213","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}
Pub Date : 2023-10-01DOI: 10.4208/jcm.2207-m2021-0349
Mingcai Ding, Xiaoliang Song and Bo Yu
{"title":"An Inexact Proximal DC Algorithm for the Large-Scale Cardinality Constrained Mean-Variance Model in Sparse Portfolio Selection","authors":"Mingcai Ding, Xiaoliang Song and Bo Yu","doi":"10.4208/jcm.2207-m2021-0349","DOIUrl":"https://doi.org/10.4208/jcm.2207-m2021-0349","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136127578","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}
Pub Date : 2023-09-01DOI: 10.4208/jcm.2301-m2022-0177
Jiayin Zhai, Xiao Li and Zhijun Shen
{"title":"A Cell-Centered Godunov Method Based on Staggered Data Distribution, Part I: One-Dimensional Case","authors":"Jiayin Zhai, Xiao Li and Zhijun Shen","doi":"10.4208/jcm.2301-m2022-0177","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2022-0177","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135349184","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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