We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.
{"title":"Optimality and duality for complex multi-objective programming","authors":"Tone-Yau Huang, Tamaki Tanaka","doi":"10.3934/naco.2021055","DOIUrl":"https://doi.org/10.3934/naco.2021055","url":null,"abstract":"We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86584962","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}
{"title":"Group sparse Bayesian learning for data-driven discovery of explicit model forms with multiple parametric datasets","authors":"Luning Sun, P. Du, Haoliang Sun, Jian-Xun Wang","doi":"10.3934/naco.2022040","DOIUrl":"https://doi.org/10.3934/naco.2022040","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87247854","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}
In this paper, we present extension of a class of split variational inequality problem and fixed point problem due to Lohawech et al. (J. Ineq Appl. 358, 2018) to a class of multiple sets split variational inequality problem and common fixed point problem (CMSSVICFP) in Hilbert spaces. Using the Halpern subgradient extragradient theorem of variational inequality problems, we propose a parallel Halpern subgradient extragradient CQ-method with adaptive step-size for solving the CMSSVICFP. We show that a sequence generated by the proposed algorithm converges strongly to the solution of the CMSSVICFP. We give a numerical example and perform some preliminary numerical tests to illustrate the numerical efficiency of our method.
本文将Lohawech et al. (J. Ineq Appl. 358, 2018)的一类分裂变分不等式问题和不动点问题推广到Hilbert空间中的一类多集分裂变分不等式问题和公共不动点问题(CMSSVICFP)。利用变分不等式问题的Halpern次梯度外扩定理，提出了求解CMSSVICFP问题的自适应步长并行Halpern次梯度外扩cq方法。我们证明了由该算法生成的序列强收敛于CMSSVICFP的解。最后给出了一个数值算例，并进行了一些初步的数值试验，以说明该方法的数值有效性。
{"title":"An adaptive block iterative process for a class of multiple sets split variational inequality problems and common fixed point problems in Hilbert spaces","authors":"H. Rehman, P. Kumam, Y. I. Suleiman, Widaya Kumam","doi":"10.3934/naco.2022007","DOIUrl":"https://doi.org/10.3934/naco.2022007","url":null,"abstract":"In this paper, we present extension of a class of split variational inequality problem and fixed point problem due to Lohawech et al. (J. Ineq Appl. 358, 2018) to a class of multiple sets split variational inequality problem and common fixed point problem (CMSSVICFP) in Hilbert spaces. Using the Halpern subgradient extragradient theorem of variational inequality problems, we propose a parallel Halpern subgradient extragradient CQ-method with adaptive step-size for solving the CMSSVICFP. We show that a sequence generated by the proposed algorithm converges strongly to the solution of the CMSSVICFP. We give a numerical example and perform some preliminary numerical tests to illustrate the numerical efficiency of our method.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85908544","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}
{"title":"Novel closed-loop controllers for fractional linear quadratic time-varying systems","authors":"Iman Malmir","doi":"10.3934/naco.2022032","DOIUrl":"https://doi.org/10.3934/naco.2022032","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83782069","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}
It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this paper, we first propose an inexact sequential injective algorithm (ISIA) for a vector equation, and show the global convergence under weak univalence assumption. Roughly speaking, the ISIA generates the sequence of inexact solutions of approximate vector equations, which consist of the injectives converging to the original vector-valued function. Although the ISIA is simple and conceptual, it can be a prototype to many other algorithms such as a smoothing Newton algorithm, semismooth Newton algorithm, etc. Next, we apply the ISIA prototype to the regularized smoothing Newton algorithm (ReSNA) for mixed second-order cone complementarity problems (MSOCCPs). Exploiting the ISIA convergence scheme, we prove that the ReSNA is globally convergent under Cartesian begin{document}$ P_0 $end{document} assumption.
It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this paper, we first propose an inexact sequential injective algorithm (ISIA) for a vector equation, and show the global convergence under weak univalence assumption. Roughly speaking, the ISIA generates the sequence of inexact solutions of approximate vector equations, which consist of the injectives converging to the original vector-valued function. Although the ISIA is simple and conceptual, it can be a prototype to many other algorithms such as a smoothing Newton algorithm, semismooth Newton algorithm, etc. Next, we apply the ISIA prototype to the regularized smoothing Newton algorithm (ReSNA) for mixed second-order cone complementarity problems (MSOCCPs). Exploiting the ISIA convergence scheme, we prove that the ReSNA is globally convergent under Cartesian begin{document}$ P_0 $end{document} assumption.
{"title":"Inexact sequential injective algorithm for weakly univalent vector equation and its application to regularized smoothing Newton algorithm for mixed second-order cone complementarity problems","authors":"S. Hayashi","doi":"10.3934/naco.2022024","DOIUrl":"https://doi.org/10.3934/naco.2022024","url":null,"abstract":"It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this paper, we first propose an inexact sequential injective algorithm (ISIA) for a vector equation, and show the global convergence under weak univalence assumption. Roughly speaking, the ISIA generates the sequence of inexact solutions of approximate vector equations, which consist of the injectives converging to the original vector-valued function. Although the ISIA is simple and conceptual, it can be a prototype to many other algorithms such as a smoothing Newton algorithm, semismooth Newton algorithm, etc. Next, we apply the ISIA prototype to the regularized smoothing Newton algorithm (ReSNA) for mixed second-order cone complementarity problems (MSOCCPs). Exploiting the ISIA convergence scheme, we prove that the ReSNA is globally convergent under Cartesian begin{document}$ P_0 $end{document} assumption.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90378420","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}
Resources scarcity and environmental degradation have made sustainable resource utilization and environmental protection worldwide. A circular economy system considers economic production activities as closed-loop feedback cycles in which resources are used sustainably and cyclically. Improving the eco-efficiency of the circular economy system has both theoretical value and practical meaning. In this work, the efficiency measurement model of the circular economy system with imprecise data based on network data envelopment analysis is proposed. The two-level mathematical programming approach is employed for measuring the system and process efficiencies. The lower and upper bounds of the efficiencies scores are calculated by transformed conventional one-level linear programs so that the existing solution methods can be applied. The proposed method is applied to assess the circular economy system of EU countries. Our results show that most countries have large difference among fuzzy efficiencies between the production efficiency and recycling efficiency stages, which reveals the source that causes the low efficiency of the circular economy system.
{"title":"Measuring efficiency of a recycling production system with imprecise data","authors":"Chengcheng Hu, Hsiao-Fan Wang, Tingyang Liu","doi":"10.3934/naco.2021052","DOIUrl":"https://doi.org/10.3934/naco.2021052","url":null,"abstract":"Resources scarcity and environmental degradation have made sustainable resource utilization and environmental protection worldwide. A circular economy system considers economic production activities as closed-loop feedback cycles in which resources are used sustainably and cyclically. Improving the eco-efficiency of the circular economy system has both theoretical value and practical meaning. In this work, the efficiency measurement model of the circular economy system with imprecise data based on network data envelopment analysis is proposed. The two-level mathematical programming approach is employed for measuring the system and process efficiencies. The lower and upper bounds of the efficiencies scores are calculated by transformed conventional one-level linear programs so that the existing solution methods can be applied. The proposed method is applied to assess the circular economy system of EU countries. Our results show that most countries have large difference among fuzzy efficiencies between the production efficiency and recycling efficiency stages, which reveals the source that causes the low efficiency of the circular economy system.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80678199","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}
R. Nigmatullin, Vadim S. Alexandrov, P. Agarwal, Shilpi Jain, Necati Ozdemir
Here, we show how to extend the possibilities of the conventional F-analysis and adapt it for quantitative description of multi-periodic signals recorded from different complex systems. The basic idea lies in filtration property of the Dirichlet function that allows finding the leading frequencies (having the predominant amplitudes) and the shortcut frequency band allows to fit the initial random signal with high accuracy (with the value of the relative error less than 5%). This modification defined as NOCFASS-approach (Non-Orthogonal Combined Fourier Analysis of the Smoothed Signals) can be applied to a wide class of different signals having multi-periodic structure. We want to underline here that the shortcut frequency dispersion has linear dependence begin{document}$ Omega_{k} = c.k+d $end{document} that differs from the conventional dispersion accepted in the conventional Fourier transformation begin{document}$ omega(k) = frac{2pi k}{T} $end{document}. (T is a period of the initial signal). With the help of integration procedure one can extract a low-frequency trend from trendless sequences that allows to applying the NOCFASS approach for calculation of the desired amplitude-frequency response (AFR) from different "noisy" random sequences. In order to underline the multi-periodic structure of random signals under analysis we consider two nontrivial examples. (a) The peculiarities of the AFR associated with Weierstrass-Mandelbrot function. (b) The random behavior of the voltammograms (VAGs) background measured for an electrochemical cell with one active electrode. We do suppose that the proposed NOCFASS-approach having new attractive properties as the simplicity of realization, agility to the problem formulated will find a wide propagation in the modern signal processing area.
在这里，我们展示了如何扩展传统f分析的可能性，并使其适应于从不同复杂系统记录的多周期信号的定量描述。其基本思想在于狄利克雷函数的滤波特性，使其能够找到领先频率(具有优势幅值)，并使其能够以较高的精度拟合初始随机信号(相对误差值小于5)%). This modification defined as NOCFASS-approach (Non-Orthogonal Combined Fourier Analysis of the Smoothed Signals) can be applied to a wide class of different signals having multi-periodic structure. We want to underline here that the shortcut frequency dispersion has linear dependence begin{document}$ Omega_{k} = c.k+d $end{document} that differs from the conventional dispersion accepted in the conventional Fourier transformation begin{document}$ omega(k) = frac{2pi k}{T} $end{document}. (T is a period of the initial signal). With the help of integration procedure one can extract a low-frequency trend from trendless sequences that allows to applying the NOCFASS approach for calculation of the desired amplitude-frequency response (AFR) from different "noisy" random sequences. In order to underline the multi-periodic structure of random signals under analysis we consider two nontrivial examples. (a) The peculiarities of the AFR associated with Weierstrass-Mandelbrot function. (b) The random behavior of the voltammograms (VAGs) background measured for an electrochemical cell with one active electrode. We do suppose that the proposed NOCFASS-approach having new attractive properties as the simplicity of realization, agility to the problem formulated will find a wide propagation in the modern signal processing area.
{"title":"Description of multi-periodic signals generated by complex systems: NOCFASS - New possibilities of the Fourier analysis","authors":"R. Nigmatullin, Vadim S. Alexandrov, P. Agarwal, Shilpi Jain, Necati Ozdemir","doi":"10.3934/naco.2022008","DOIUrl":"https://doi.org/10.3934/naco.2022008","url":null,"abstract":"Here, we show how to extend the possibilities of the conventional F-analysis and adapt it for quantitative description of multi-periodic signals recorded from different complex systems. The basic idea lies in filtration property of the Dirichlet function that allows finding the leading frequencies (having the predominant amplitudes) and the shortcut frequency band allows to fit the initial random signal with high accuracy (with the value of the relative error less than 5%). This modification defined as NOCFASS-approach (Non-Orthogonal Combined Fourier Analysis of the Smoothed Signals) can be applied to a wide class of different signals having multi-periodic structure. We want to underline here that the shortcut frequency dispersion has linear dependence begin{document}$ Omega_{k} = c.k+d $end{document} that differs from the conventional dispersion accepted in the conventional Fourier transformation begin{document}$ omega(k) = frac{2pi k}{T} $end{document}. (T is a period of the initial signal). With the help of integration procedure one can extract a low-frequency trend from trendless sequences that allows to applying the NOCFASS approach for calculation of the desired amplitude-frequency response (AFR) from different \"noisy\" random sequences. In order to underline the multi-periodic structure of random signals under analysis we consider two nontrivial examples. (a) The peculiarities of the AFR associated with Weierstrass-Mandelbrot function. (b) The random behavior of the voltammograms (VAGs) background measured for an electrochemical cell with one active electrode. We do suppose that the proposed NOCFASS-approach having new attractive properties as the simplicity of realization, agility to the problem formulated will find a wide propagation in the modern signal processing area.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90942890","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}
For signal enhancement, beamforming remains to be an essential technique for many applications. In the design process, the microphone locations are prescribed and the signal from a target location is being enhanced. While the filter coefficients can be readily optimized, it is found that the signal enhancement capability depends significantly on the array configuration. Therefore, it is advantageous to consider both filters and microphone positions as design variables. In this paper, this problem is addressed. We formulate the beamformer design problem as a non-linear least square problem and propose Gauss-Newton algorithm to update both filters and configuration simultaneously during iterations. We illustrate by several designs to demonstrate the effectiveness of the proposed method.
{"title":"On the simultaneous design of broadband beamformer filters and configuration","authors":"M. Gao, Ka-Fai Cedric Yiu","doi":"10.3934/naco.2022019","DOIUrl":"https://doi.org/10.3934/naco.2022019","url":null,"abstract":"For signal enhancement, beamforming remains to be an essential technique for many applications. In the design process, the microphone locations are prescribed and the signal from a target location is being enhanced. While the filter coefficients can be readily optimized, it is found that the signal enhancement capability depends significantly on the array configuration. Therefore, it is advantageous to consider both filters and microphone positions as design variables. In this paper, this problem is addressed. We formulate the beamformer design problem as a non-linear least square problem and propose Gauss-Newton algorithm to update both filters and configuration simultaneously during iterations. We illustrate by several designs to demonstrate the effectiveness of the proposed method.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82708983","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}
Pre-sale policy is a frequently-used sales approach for deteriorating products, e.g, fruits, vegetables, seafood, etc. In this paper, we consider an EOQ inventory model under pre-sale policy for deteriorating products, in which the demand of pre-sale period depends on price and pre-sale horizon, and the demand of spot-sale period depends on the price and stock level. Optimal pricing decisions and economic order quantity are also provided. We compare pre-sale model with a benchmark inventory model in which all the products are sold in spot-sale period. Theoretical results are derived to show the existence and uniqueness of the optimal solution. Numerical experiments are carried out to to illustrate the theoretical results. And sensitivity analysis is conducted to identify conditions under which the pre-sale policy is better off than the spot-sale only policy.
{"title":"Optimal pre-sale policy for deteriorating items","authors":"Lianxia Zhao, H. Qiao, Q. An","doi":"10.3934/naco.2021054","DOIUrl":"https://doi.org/10.3934/naco.2021054","url":null,"abstract":"Pre-sale policy is a frequently-used sales approach for deteriorating products, e.g, fruits, vegetables, seafood, etc. In this paper, we consider an EOQ inventory model under pre-sale policy for deteriorating products, in which the demand of pre-sale period depends on price and pre-sale horizon, and the demand of spot-sale period depends on the price and stock level. Optimal pricing decisions and economic order quantity are also provided. We compare pre-sale model with a benchmark inventory model in which all the products are sold in spot-sale period. Theoretical results are derived to show the existence and uniqueness of the optimal solution. Numerical experiments are carried out to to illustrate the theoretical results. And sensitivity analysis is conducted to identify conditions under which the pre-sale policy is better off than the spot-sale only policy.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75845484","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}
Xin He Miao, Kai Yao, Ching-Yu Yang, Jein-Shan Chen
In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indicates that the proposed algorithm could also be a good choice for solving the SOCAVE.
{"title":"Levenberg-Marquardt method for absolute value equation associated with second-order cone","authors":"Xin He Miao, Kai Yao, Ching-Yu Yang, Jein-Shan Chen","doi":"10.3934/naco.2021050","DOIUrl":"https://doi.org/10.3934/naco.2021050","url":null,"abstract":"In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indicates that the proposed algorithm could also be a good choice for solving the SOCAVE.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76238240","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}
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