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Quartic Regularity. 四次规律性。
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2025-01-01 Epub Date: 2025-03-12 DOI: 10.1007/s10013-024-00720-z
Yurii Nesterov
{"title":"Quartic Regularity.","authors":"Yurii Nesterov","doi":"10.1007/s10013-024-00720-z","DOIUrl":"10.1007/s10013-024-00720-z","url":null,"abstract":"<p><p>In this paper, we propose new linearly convergent second-order methods for minimizing convex quartic polynomials. This framework is applied for designing optimization schemes, which can solve general convex problems satisfying a new condition of quartic regularity. It assumes positive definiteness and boundedness of the fourth derivative of the objective function. For such problems, an appropriate quartic regularization of Damped Newton Method has global linear rate of convergence. We discuss several important consequences of this result. In particular, it can be used for constructing new second-order methods in the framework of high-order proximal-point schemes (Nesterov, Math. Program. <b>197</b>, 1-26, 2023 and Nesterov, SIAM J. Optim. <b>31</b>, 2807-2828, 2021). These methods have convergence rate <math> <mrow><mover><mi>O</mi> <mo>~</mo></mover> <mrow><mo>(</mo> <msup><mi>k</mi> <mrow><mo>-</mo> <mi>p</mi></mrow> </msup> <mo>)</mo></mrow> </mrow> </math> , where <i>k</i> is the iteration counter, <i>p</i> is equal to 3, 4, or 5, and tilde indicates the presence of logarithmic factors in the complexity bounds for the auxiliary problems, which are solved at each iteration of the schemes.</p>","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"53 3","pages":"553-575"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12202589/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144530292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Index Divisors and Monogenity of Certain Sextic Number Fields Defined by $$x^6+ax^5+b$$ 论由 $$x^6+ax^5+b$$ 定义的某些六元数域的索引除数和单原性
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2024-01-10 DOI: 10.1007/s10013-023-00679-3
L. El Fadil, O. Kchit
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引用次数: 0
An Improved Adaptive Meshless Refinement for the RBF-FD Method for 2D Elliptic Equations 二维椭圆方程 RBF-FD 方法的改进型自适应无网格细化
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2024-01-10 DOI: 10.1007/s10013-023-00678-4
Oanh Thi Dang
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引用次数: 0
Correction: Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part 更正：具有 BMO 反对称部分的二阶椭圆算子的扰动理论
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2024-01-09 DOI: 10.1007/s10013-023-00669-5
M. Dindoš, Erik Sätterqvist, Martin Ulmer
{"title":"Correction: Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part","authors":"M. Dindoš, Erik Sätterqvist, Martin Ulmer","doi":"10.1007/s10013-023-00669-5","DOIUrl":"https://doi.org/10.1007/s10013-023-00669-5","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"24 8","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform Regularity Estimates for Three Dimensional Nonhomogeneous Incompressible Heat Conducting Navier–Stokes Flows 三维非均质导热纳维-斯托克斯流的均匀正则性估计
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2024-01-04 DOI: 10.1007/s10013-023-00676-6
S. Gala, M. Théra
{"title":"Uniform Regularity Estimates for Three Dimensional Nonhomogeneous Incompressible Heat Conducting Navier–Stokes Flows","authors":"S. Gala, M. Théra","doi":"10.1007/s10013-023-00676-6","DOIUrl":"https://doi.org/10.1007/s10013-023-00676-6","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"3 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139384388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Irreducibility of p-Adic Banach Principal Series of p-Adic $$textrm{GL}_3$$ 论 p-Adic $$textrm{GL}_3$ 的 p-Adic Banach 主数列的不可重复性
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2024-01-04 DOI: 10.1007/s10013-023-00675-7
Noriyuki Abe, Florian Herzig
{"title":"On the Irreducibility of p-Adic Banach Principal Series of p-Adic $$textrm{GL}_3$$","authors":"Noriyuki Abe, Florian Herzig","doi":"10.1007/s10013-023-00675-7","DOIUrl":"https://doi.org/10.1007/s10013-023-00675-7","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"56 40","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139384733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-Posedness for the Extended Schrödinger–Benjamin–Ono System 扩展薛定谔-本杰明-奥诺系统的良好假设性
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2023-12-06 DOI: 10.1007/s10013-023-00664-w
Felipe Linares, Argenis J. Mendez, D. Pilod
{"title":"Well-Posedness for the Extended Schrödinger–Benjamin–Ono System","authors":"Felipe Linares, Argenis J. Mendez, D. Pilod","doi":"10.1007/s10013-023-00664-w","DOIUrl":"https://doi.org/10.1007/s10013-023-00664-w","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"67 42","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138594846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Signed and Sign-Changing Solutions for a Kirchhoff-Type Problem Involving the Weighted N-Laplacian with Critical Double Exponential Growth 涉及临界双指数增长加权 N-拉普拉卡方的基尔霍夫式问题的符号和符号变化解法
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2023-12-02 DOI: 10.1007/s10013-023-00667-7
Sami Baraket, Rima Chetouane, Rached Jaidane
{"title":"Signed and Sign-Changing Solutions for a Kirchhoff-Type Problem Involving the Weighted N-Laplacian with Critical Double Exponential Growth","authors":"Sami Baraket, Rima Chetouane, Rached Jaidane","doi":"10.1007/s10013-023-00667-7","DOIUrl":"https://doi.org/10.1007/s10013-023-00667-7","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"68 11","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138606473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of Weakly Compact Multipliers on Left $$phi $$-Amenable Banach Algebras 左$$phi$$可矢量巴拿赫数组上弱紧凑乘数的表征
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2023-12-02 DOI: 10.1007/s10013-023-00662-y
S. Soltani Renani, Z. Yari
{"title":"Characterization of Weakly Compact Multipliers on Left $$phi $$-Amenable Banach Algebras","authors":"S. Soltani Renani, Z. Yari","doi":"10.1007/s10013-023-00662-y","DOIUrl":"https://doi.org/10.1007/s10013-023-00662-y","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"118 46","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138607240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Stability of Shear Flows in Bounded Channels, II: Non-monotonic Shear Flows 论有界水道中剪切流的稳定性，II：非单调剪切流
IF 0.8
Vietnam Journal of Mathematics Pub Date : 2023-11-29 DOI: 10.1007/s10013-023-00661-z
Alexandru D. Ionescu, Sameer Iyer, Hao Jia
{"title":"On the Stability of Shear Flows in Bounded Channels, II: Non-monotonic Shear Flows","authors":"Alexandru D. Ionescu, Sameer Iyer, Hao Jia","doi":"10.1007/s10013-023-00661-z","DOIUrl":"https://doi.org/10.1007/s10013-023-00661-z","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139213509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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