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A comparative study of the PL homotopy and BFGS methods for some nonsmooth optimization problems 一类非光滑优化问题的PL同伦与BFGS方法的比较研究
Creative Mathematics and Informatics Pub Date : 2019-06-23 DOI: 10.37193/cmi.2019.02.01
Andrei Bozantan, V. Berinde
{"title":"A comparative study of the PL homotopy and BFGS methods for some nonsmooth optimization problems","authors":"Andrei Bozantan, V. Berinde","doi":"10.37193/cmi.2019.02.01","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.01","url":null,"abstract":"We consider some non-smooth functions and investigate the numerical behavior of the Piecewise Linear Hompotopy (PLH) method ([Bozântan, A., An implementation of the piecewise-linear homotopy algorithm for the computation of fixed points, Creat. Math. Inform., 19 (2010), No.~2, 140–148] and [Bozântan, A. and Berinde, V., Applications of the PL homotopy algorithm for the computation of fixed points to unconstrained optimization problems, Creat. Math. Inform., 22 (2013), No. 1, 41–46]). We compare the PLH method with the BFGS with inexact line search, a quasi-Newton method, having some results reported in [Lewis, A. S. and Overton, M. L., Nonsmooth optimization via BFGS, submitted to SIAM J. Optimiz, (2009)]. For most of the considered cases, the characteristics of the PLH method are quite similar to the BFGS method, that is, the PLH method converges to local minimum values and the convergence rate seems to be linear with respect to the number of function evaluations, but we also identify some issues with the PLH method.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123576210","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
Note on the paper “An improvement of Batir’s asymptotic formula and some estimates related to the gamma function” 关于“对Batir渐近公式的改进及与伽马函数有关的一些估计”一文的注解
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/cmi.2019.02.14
Sorin-Adrian Dumitrescu
{"title":"Note on the paper “An improvement of Batir’s asymptotic formula and some estimates related to the gamma function”","authors":"Sorin-Adrian Dumitrescu","doi":"10.37193/cmi.2019.02.14","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.14","url":null,"abstract":"The aim of this note is to correct a result given in [Cristea, V. C. and Dumitrescu, S., An improvement of Batir’s asymptotic formula and some estimates\u0000related to the gamma function, Creat. Math. Inform., 25 (2016), No. 2 165–173].","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114471563","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
A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces Banach空间中多值拟非扩张映射不动点的改进Krasnosellkii-Mann算法
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/cmi.2019.02.10
T. Sow
{"title":"A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces","authors":"T. Sow","doi":"10.37193/cmi.2019.02.10","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.10","url":null,"abstract":"It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces.\u0000Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper\u0000are significant improvement on important recent results.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"254 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115094181","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
Reduction approach to second order perturbed state-dependent sweeping process 二阶状态相关摄动清扫过程的约简方法
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/cmi.2019.02.13
M. Yarou
{"title":"Reduction approach to second order perturbed state-dependent sweeping process","authors":"M. Yarou","doi":"10.37193/cmi.2019.02.13","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.13","url":null,"abstract":"In this paper, we present a new approach to solving second order nonconvex perturbed sweeping process in finite dimensional setting. It consists in a reduction of the problem to a first order one without use of the standard methods of fixed point theory. The perturbation, that is the external force applied on the system is not necessary with bounded values.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117013192","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: 5
Wijsman quasi-invariant convergence Wijsman拟不变收敛
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/cmi.2019.02.03
Esra Gulle, Uǧur Ulusu
{"title":"Wijsman quasi-invariant convergence","authors":"Esra Gulle, Uǧur Ulusu","doi":"10.37193/cmi.2019.02.03","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.03","url":null,"abstract":"In this study, we defined concepts of Wijsman quasi-invariant convergence, Wijsman quasi-strongly invariant convergence and Wijsman quasi-strongly q-invariant convergence. Also, we give the concept of Wijsman quasi-invariant statistically convergence. Then, we study relationships among these concepts. Furthermore, we investigate relationship between these concepts and some convergence types given earlier for sequences of sets, too.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124055336","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: 1
On the existence of antiderivatives of some real functions 若干实函数不定积分的存在性
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/cmi.2019.02.11
I. Tascu
{"title":"On the existence of antiderivatives of some real functions","authors":"I. Tascu","doi":"10.37193/cmi.2019.02.11","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.11","url":null,"abstract":"An antiderivative of a real function f(x) defined on an interval I ⊂ R is a function F(x) whose derivative is equal to f(x), that is, F\u00000\u0000(x) = f(x),\u0000for all x ∈ I. Antidifferentiation is the process of finding the set of all antiderivatives of a given function. If f and g are defined on the same interval\u0000I, then the set of antiderivatives of the sum of f and g equals the sum of the general antiderivatives of f and g. In general, the antiderivatives\u0000of the product of two functions f and g do not coincide to the product of the antiderivatives of f and g. Moreover, the fact that f and g have\u0000antiderivatives does not imply that the product f · g has antiderivatives. Our aim in this paper is to present some conditions which ensure that\u0000the product f · g and the composition f ◦ g of two functions f and g has antiderivatives.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123960994","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
Sums and spectral norms of all almost balancing numbers 所有几乎平衡数的和和和谱范数
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/cmi.2019.02.12
A. Tekcan
{"title":"Sums and spectral norms of all almost balancing numbers","authors":"A. Tekcan","doi":"10.37193/cmi.2019.02.12","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.12","url":null,"abstract":"In this work, we derive some algebraic relations on sums of all almost balancing numbers of first and second type. We also deduce some formulas\u0000on sums of Pell, Pell–Lucas and balancing numbers in terms of all almost balancing numbers of first and second type. Further, we formulate the\u0000eigenvalues and spectral norms of circulant matrices of all almost balancing numbers of first and second type.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"27 19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134106617","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: 2
Existence of countably many symmetric positive solutions for system of even order time scale boundary value problems in Banach spaces Banach空间中偶阶时标边值问题系统的可数多对称正解的存在性
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/cmi.2019.02.08
K. R. Prasad, Muhammad Khuddush
{"title":"Existence of countably many symmetric positive solutions for system of even order time scale boundary value problems in Banach spaces","authors":"K. R. Prasad, Muhammad Khuddush","doi":"10.37193/cmi.2019.02.08","DOIUrl":"https://doi.org/10.37193/cmi.2019.02.08","url":null,"abstract":"Existence of countably many symmetric positive solutions for system of even order time scale boundary value problems in Banach spaces","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130634662","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
Distance based topological descriptors for two classes of graphs 两类图的基于距离的拓扑描述符
Creative Mathematics and Informatics Pub Date : 2019-06-19 DOI: 10.37193/CMI.2019.02.07
K. Pattabiraman
{"title":"Distance based topological descriptors for two classes of graphs","authors":"K. Pattabiraman","doi":"10.37193/CMI.2019.02.07","DOIUrl":"https://doi.org/10.37193/CMI.2019.02.07","url":null,"abstract":"In this paper, the exact formula for the generalized product degree distance, reciprocal product degree distance and product degree distance of\u0000Mycielskian graph and its complement are obtained. In addition, we compute the above indices for non-commuting graph.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126266252","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 Wijsman asymptotically lacunary I-statistical equivalence of weight g of sequence of sets 集序列权g的Wijsman渐近缺i统计等价
Creative Mathematics and Informatics Pub Date : 2019-03-01 DOI: 10.37193/cmi.2019.01.09
Ö. Kişi
{"title":"On Wijsman asymptotically lacunary I-statistical equivalence of weight g of sequence of sets","authors":"Ö. Kişi","doi":"10.37193/cmi.2019.01.09","DOIUrl":"https://doi.org/10.37193/cmi.2019.01.09","url":null,"abstract":"This paper presents the following definition which is a natural combination of the definitions of asymptotically equivalence, I-convergence, statistical limit, lacunary sequence, and Wijsman convergence of weight g; where g : N → [0,∞) is a function satisfying limn→∞ g (n) = ∞ and n g(n) 9 0 as n → ∞ for sequence of sets. Let (X, ρ) be a metric space, θ = {kr} be a lacunary sequence and I ⊆ 2N be an admissible ideal. For any non-empty closed subsets Ak, Bk ⊆ X such that d(x,Ak) > 0 and d(x,Bk) > 0 for each x ∈ X , we say that the sequences {Ak} and {Bk} are Wijsman I-asymptotically lacunary statistical equivalent of multiple L of weight g if for every ε > 0, δ > 0 and for each x ∈ X, { r ∈ N : 1 g (hr) ∣∣∣∣{k ∈ Ir : ∣∣∣∣d(x,Ak) d(x,Bk) − L ∣∣∣∣ ≥ ε}∣∣∣∣ ≥ δ} ∈ I (denoted byAk S θ (IW ) g ∼ Bk ). We mainly investigate their relationship and also make some observations about these classes.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130521019","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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