Applied Mathematics and Computation最新文献

{"title":"Nonlinear conjugate gradient method for vector optimization on Riemannian manifolds with retraction and vector transport","authors":"Kangming Chen ,&nbsp;Ellen Hidemi Fukuda ,&nbsp;Hiroyuki Sato","doi":"10.1016/j.amc.2024.129001","DOIUrl":"10.1016/j.amc.2024.129001","url":null,"abstract":"<div><p>In this paper, we propose nonlinear conjugate gradient methods for vector optimization on Riemannian manifolds. The concepts of Wolfe and Zoutendjik conditions are extended to Riemannian manifolds. Specifically, the existence of intervals of step sizes that satisfy the Wolfe conditions is established. The convergence analysis covers the vector extensions of the Fletcher–Reeves, conjugate descent, and Dai–Yuan parameters. Under some assumptions, we prove that the sequence obtained by the proposed algorithm can converge to a Pareto stationary point. Moreover, several other choices of the parameter are discussed. Numerical experiments illustrating the practical behavior of the methods are presented.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122846","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":"Improved algorithm for the optimal quantization of single- and multivariate random functions","authors":"Liyang Ma ,&nbsp;Daniel Conus ,&nbsp;Wei-Min Huang ,&nbsp;Paolo Bocchini","doi":"10.1016/j.amc.2024.129028","DOIUrl":"10.1016/j.amc.2024.129028","url":null,"abstract":"<div><p>The Functional Quantization (FQ) method was developed for the approximation of random processes with optimally constructed finite sets of deterministic functions (quanta) and associated probability masses. The quanta and the corresponding probability masses are collectively called a “<em>quantizer</em>”. A method called “Functional Quantization by Infinite-Dimensional Centroidal Voronoi Tessellation” (FQ-IDCVT) was developed for the numerical implementation of FQ. Compared to other methodologies, the FQ-IDCVT algorithm has the advantages of versatility, simplicity, and ease of application. The FQ-IDCVT algorithm was proved to be able to capture the overall stochastic characteristics of random processes. However, for certain time instants of the processes, the FQ-IDCVT algorithm may fail in approximating well the stochastic properties, which results in significant local errors. For instance, it may significantly underestimate the variances and overestimate the correlation coefficients for some time instants. In addition, the FQ concept was developed for the quantization of single-variate processes. A formal description of its application to multivariate processes is lacking in the literature. Therefore, this paper has two objectives: to extend the FQ concept to multivariate processes and to enhance the FQ-IDCVT algorithm so that its accuracy is more uniform across the various time instants for single-variate processes and applicable to multivariate processes. Along this line, the limitations of the FQ-IDCVT algorithm are explained, and a novel improved FQ-IDCVT algorithm is proposed. Four criteria are introduced to quantify the algorithms' global and local quantization performance. For illustration and validation purposes, four numerical examples of single-variate and multivariate, stationary and non-stationary processes with Gaussian and non-Gaussian marginal distributions were quantized. The results of the numerical examples demonstrate the performance and superiority of the proposed algorithm compared to the original FQ-IDCVT algorithm.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122649","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":"Adaptive distributed unknown input observer for linear systems","authors":"Dan-Dan Zhou ,&nbsp;Ran Zhao","doi":"10.1016/j.amc.2024.129027","DOIUrl":"10.1016/j.amc.2024.129027","url":null,"abstract":"<div><p>This paper studies the adaptive distributed unknown input observer (ADUIO) for linear systems with local outputs, which contains a group of local observers under directed graph. The difficulty is the adaptive estimation of global output for the systems with unknown inputs. To solve the problem, disturbance decoupling principle and leader-following consensus strategy are integrated to estimate local outputs of other observers, which can be accumulated to recover the global outputs. Based on the estimated global outputs, an ADUIO is constructed to estimate the full state which avoids using local output matrices of other observers and global information of the graph. Different from the extensive joint detectability assumption in existing results, a detectability assumption is given to make the estimation errors converge to zero asymptotically.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099483","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":"Vector multispaces and multispace codes","authors":"Mladen Kovačević","doi":"10.1016/j.amc.2024.129041","DOIUrl":"10.1016/j.amc.2024.129041","url":null,"abstract":"<div><p>Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than 1 are derived. An application in coding theory is illustrated by showing that multispace codes that are introduced here may be used in random linear network coding scenarios, and that they generalize standard subspace codes (defined in the set of all subspaces of <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>) and extend them to an infinitely larger set of parameters. In particular, in contrast to subspace codes, multispace codes of arbitrarily large cardinality and minimum distance exist for any fixed <em>n</em> and <em>q</em>.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099484","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":"Analytically pricing volatility options and capped/floored volatility swaps with nonlinear payoffs in discrete observation case under the Merton jump-diffusion model driven by a nonhomogeneous Poisson process","authors":"Sanae Rujivan","doi":"10.1016/j.amc.2024.129029","DOIUrl":"10.1016/j.amc.2024.129029","url":null,"abstract":"<div><p>In this paper, we introduce novel analytical solutions for valuating volatility derivatives, including volatility options and capped/floored volatility swaps, employing discrete sampling within the framework of the Merton jump-diffusion model, which is driven by a nonhomogeneous Poisson process. The absence of a comprehensive understanding of the probability distribution characterizing the realized variance has historically impeded the development of a robust analytical valuation approach for such instruments. Through the application of the cumulative distribution function of the realized variance conditional on Poisson jumps, we have derived explicit expectations for the derivative payoffs articulated as functions of the extremum values of the square root of the realized variance. We delineate precise pricing structures for an array of instruments, encompassing variance and volatility swaps, variance and volatility options, and their respective capped and floored variations, alongside establishing put-call parity and relationships for capped and floored positions. Complementing the theoretical advancements, we substantiate the practical efficacy and precision of our solutions via Monte Carlo simulations, articulated through multiple numerical examples. Conclusively, our analysis extends to the quantification of jump impacts on the fair strike prices of volatility derivatives with nonlinear payoffs, facilitated by our analytic pricing expressions.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099482","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 fast local search based memetic algorithm for the parallel row ordering problem","authors":"Gintaras Palubeckis","doi":"10.1016/j.amc.2024.129040","DOIUrl":"10.1016/j.amc.2024.129040","url":null,"abstract":"<div><p>The parallel row ordering problem (PROP) is concerned with arranging two groups of facilities along two parallel lines with the goal of minimizing the sum of the flow cost-weighted distances between the pairs of facilities. As the main result of this paper, we show that the insertion neighborhood for the PROP can be explored in optimal time <span><math><mi>Θ</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> by providing an <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>-time procedure for performing this task, where <em>n</em> is the number of facilities. As a case study, we incorporate this procedure in a memetic algorithm (MA) for solving the PROP. We report on numerical experiments that we conducted with MA on PROP instances with up to 500 facilities. The experimental results demonstrate that the MA is superior to the adaptive iterated local search algorithm and the parallel hyper heuristic method, which are state-of-the-art for the PROP. Remarkably, our algorithm improved best known solutions for six largest instances in the literature. We conjecture that the time complexity of exploring the interchange neighborhood for the PROP is <span><math><mi>Θ</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, exactly as in the case of insertion operation.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089071","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":"Exponential stability of switched systems with state-dependent delayed impulses via B-equivalent method","authors":"Qian Cui ,&nbsp;Jinde Cao ,&nbsp;Lulu Li ,&nbsp;Yang Liu","doi":"10.1016/j.amc.2024.129031","DOIUrl":"10.1016/j.amc.2024.129031","url":null,"abstract":"<div><p>This paper studies the stability problem of switched systems with state-dependent delayed impulses (SDDIs), where switching times satisfy the definition of average dwell-time. Firstly, the pulse phenomenon of the systems with SDDIs is avoided under some necessary assumptions. Subsequently, the state-dependent delayed impulsive switched systems can be transformed into the corresponding time-dependent ones by using the B-equivalent method. Furthermore, the stability of stable and unstable systems with time-dependent delayed impulses (TDDIs) are analyzed, where the limitation that the impulsive delays are less than the impulsive intervals is relaxed. Based on the equivalence of the original system and the corresponding switched system with TDDIs, some new stability conditions for the switched systems with SDDIs are derived. Finally, the theoretical results are applied to a switched neural network with SDDIs to demonstrate the validity of the results.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089070","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":"Non-fragile output-feedback control for delayed memristive bidirectional associative memory neural networks against actuator failure","authors":"R. Suvetha ,&nbsp;J.J. Nieto ,&nbsp;P. Prakash","doi":"10.1016/j.amc.2024.129021","DOIUrl":"10.1016/j.amc.2024.129021","url":null,"abstract":"<div><p>This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals in the actuator received from the fluctuated controller, control gain matrices encompass situations intended to memory non-fragile output-feedback controller. Based on the Lyapunov stability theory, differential inclusion theory, and congruence transformation, the sufficient condition for the global asymptotic stabilization property for the designed fault-tolerant memristive bidirectional associative memory neural network model is obtained in terms of linear matrix inequality by utilizing Wirtinger's inequality. Finally, numerical examples are approached with the state performance plots of the proposed memristive bidirectional associative memory neural network model with respect to the time-domain plane, to confirm the stabilization results and it illustrates the working mechanism of the designed controller.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084069","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":"Modelling the prevalence of prostitution under the influence of poverty: A deterministic vs. stochastic approach","authors":"G. Divya ,&nbsp;S. Athithan ,&nbsp;Mini Ghosh","doi":"10.1016/j.amc.2024.129030","DOIUrl":"10.1016/j.amc.2024.129030","url":null,"abstract":"<div><p>Globally, there is a widespread awareness of poverty-related challenges. It's important to acknowledge that poverty is one of the key factors influencing prostitution. Addressing the rise in prostitution due to economic challenges is a major concern among the general public. In that scenario, many poor family girls/women were ready to downgrade their status for their family welfare and necessary needs. On that aspect, they are indulging in prostitution also because of their inability to do any other work. Particularly in the pandemic and lockdown, the situation is worsening for such people. To overcome these challenges, multi-angled and effective approaches have been adopted. We have formulated a nonlinear mathematical model to investigate the dynamics around prostitution due to impoverishment. Our model exhibits two equilibrium points, which are analyzed through a stability analysis. The threshold <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> has determined and investigated its significant parameters for the spread of prostitution through numerical simulation. Further, we extended this model to a stochastic model to know its real nature. We have examined and contrasted the deterministic and stochastic outcomes pertaining to the behavior of significant parameters within this model. Our findings show better results in both the deterministic and stochastic natures. Moreover, we calibrated our model using data on sex workers. Our projections, derived from this fitting process, suggest a subsequent decline in the sex-worker population after 2023.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084068","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":"Exploring redundant trees in bipartite graphs","authors":"Qing Yang,&nbsp;Yingzhi Tian","doi":"10.1016/j.amc.2024.129006","DOIUrl":"10.1016/j.amc.2024.129006","url":null,"abstract":"<div><p>Luo et al. conjectured that for a tree <em>T</em> with bipartition <em>X</em> and <em>Y</em>, if a <em>k</em>-connected bipartite graph <em>G</em> with minimum degree at least <span><math><mi>k</mi><mo>+</mo><mi>max</mi><mo>⁡</mo><mo>{</mo><mo>|</mo><mi>X</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>}</mo></math></span>, then <em>G</em> has a subtree <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> isomorphic to <em>T</em> such that <span><math><mi>G</mi><mo>−</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>)</mo></math></span> is <em>k</em>-connected. Although this conjecture has been validated for spiders and caterpillars in cases where <span><math><mi>k</mi><mo>≤</mo><mn>3</mn></math></span>, and also for paths with odd order, its general applicability has remained an open question. In this paper, we establish the validity of this conjecture for <span><math><mi>k</mi><mo>≤</mo><mn>3</mn></math></span> with the girth under of <em>G</em> at least the diameter of <em>G</em> minus one.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089069","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}