Journal of Complexity最新文献

{"title":"On the information complexity for integration in subspaces of the Wiener algebra","authors":"Liang Chen, Haixin Jiang","doi":"10.1016/j.jco.2023.101819","DOIUrl":"10.1016/j.jco.2023.101819","url":null,"abstract":"<div><p>Recently, Goda proved the polynomial tractability of integration on the following function subspace of the Wiener algebra<span><span><span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>:</mo><mo>=</mo><mrow><mo>{</mo><mi>f</mi><mo>∈</mo><mi>C</mi><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo><mo>|</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub></mrow><mspace></mspace><mspace></mspace><mspace></mspace><mo>:</mo><mo>=</mo><munder><mo>∑</mo><mrow><mi>k</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></munder><mo>|</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>k</mi><mo>)</mo><mo>|</mo><mi>max</mi><mo>⁡</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><munder><mi>min</mi><mrow><mi>j</mi><mo>∈</mo><mi>supp</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></munder><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>|</mo><mo>)</mo></mrow><mo><</mo><mo>∞</mo><mo>}</mo><mo>,</mo></math></span></span></span> where <span><math><mi>T</mi><mo>:</mo><mo>=</mo><mi>R</mi><mo>/</mo><mi>Z</mi><mo>=</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>k</mi><mo>)</mo></math></span> is the <strong><em>k</em></strong><span>-th Fourier coefficient of </span><em>f</em> and <span><math><mi>supp</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>{</mo><mi>j</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>d</mi><mo>}</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>≠</mo><mn>0</mn><mo>}</mo></math></span>. Goda raised an open question as to whether the upper bound of the information complexity for integration in <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span><span> can be improved. In this note, we give a positive answer. By establishing a Monte Carlo sampling method and using Rademacher complexity to estimate the uniform convergence rate, the upper bound can be improved to </span><span><math><mi>Θ</mi><mo>(</mo><mi>d</mi><mo>/</mo><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span>, where <span><math><mi>ϵ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></math></span> is the target accuracy. We also use the same technique to estimate the information complexity for a Hölder continuous subspace of Wiener algebra. Compared to the previous upper bound <span><math><mi>Θ</mi><mo>(</mo><mi>max</mi><mo>⁡</mo><mo>(</mo><mfrac><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo><mfrac><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>q</mi></mrow></","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"81 ","pages":"Article 101819"},"PeriodicalIF":1.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139071325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A duality approach to regularized learning problems in Banach spaces","authors":"Raymond Cheng ,&nbsp;Rui Wang ,&nbsp;Yuesheng Xu","doi":"10.1016/j.jco.2023.101818","DOIUrl":"10.1016/j.jco.2023.101818","url":null,"abstract":"<div><p><span>Regularized learning problems in Banach spaces, which often minimize the sum of a data fidelity term in one Banach norm and a </span>regularization<span><span> term in another Banach norm, is challenging to solve. We construct a direct sum space based on the Banach spaces for the fidelity term and the regularization term, and recast the objective function as the norm of a quotient space of the direct sum space. We then express the original regularized problem as an optimization problem in the dual space of the direct sum space. It is to find the maximum of a linear function on a convex polytope, which may be solved by linear programming. A solution of the original problem is then obtained by using related </span>extremal properties of norming functionals from a solution of the dual problem. Numerical experiments demonstrate that the proposed duality approach is effective for solving the regularization learning problems.</span></p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"81 ","pages":"Article 101818"},"PeriodicalIF":1.7,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal recovery and volume estimates","authors":"A. Kushpel","doi":"10.1016/j.jco.2023.101780","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101780","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"177 1","pages":"101780"},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54746253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The rate of convergence for sparse and low-rank quantile trace regression","authors":"Xiangyong Tan, Ling Peng, Peiwen Xiao, Qing Liu, Xiaohui Liu","doi":"10.1016/j.jco.2023.101778","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101778","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"79 1","pages":"101778"},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54746217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Changes of the Editorial Board","authors":"Eric Novak","doi":"10.1016/j.jco.2023.101792","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101792","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"206 1","pages":"101792"},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54746309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the complexity of a unified convergence analysis for iterative methods","authors":"I. Argyros, S. Shakhno, Samundra Regmi, H. Yarmola","doi":"10.1016/j.jco.2023.101781","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101781","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"79 1","pages":"101781"},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54746283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a unified convergence analysis for Newton-type methods solving generalized equations with the Aubin property","authors":"Ioannis K. Argyros ,&nbsp;Santhosh George","doi":"10.1016/j.jco.2023.101817","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101817","url":null,"abstract":"<div><p>A plethora of applications from diverse disciplines reduce to solving generalized equations involving Banach space<span> valued operators. These equations are solved mostly iteratively, when a sequence is generated approximating a solution provided that certain conditions are valid on the starting point and the operators appearing on the method. Secant-type methods are developed whose specializations reduce to well known methods such as Newton, modified Newton, Secant<span>, Kurchatov and Steffensen<span><span> to mention a few. Unified local as well as semi-local analysis of these methods is presented using the celebrated contraction mapping principle in combination with the Aubin property of a set valued operator, and generalized continuity assumption on the operators on these methods. </span>Numerical applications complement the theory.</span></span></span></p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"81 ","pages":"Article 101817"},"PeriodicalIF":1.7,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138471557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal recovery and generalized Carlson inequality for weights with symmetry properties","authors":"K.Yu. Osipenko","doi":"10.1016/j.jco.2023.101807","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101807","url":null,"abstract":"<div><p>The paper concerns problems of the recovery of operators from noisy information in weighted<!--> <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>-spaces<!--> <!-->with<!--> <!-->homogeneous<!--> <!-->weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-metric.</p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"81 ","pages":"Article 101807"},"PeriodicalIF":1.7,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92121785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Changes of the Editorial Board","authors":"Erich Novak","doi":"10.1016/j.jco.2023.101806","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101806","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"80 ","pages":"Article 101806"},"PeriodicalIF":1.7,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49887913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kateryna Pozharska is the winner of the 2023 Joseph F. Traub Information-Based Complexity Young Researcher Award","authors":"David Krieg,&nbsp;Erich Novak,&nbsp;Mathias Sonnleitner,&nbsp;Michaela Szölgyenyi,&nbsp;Henryk Woźniakowski","doi":"10.1016/j.jco.2023.101805","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101805","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"80 ","pages":"Article 101805"},"PeriodicalIF":1.7,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49887912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}