Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stocha...Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.展开更多
In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multiplie...In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multipliers (ADMM), is employed to solve such problems typically, which still requires the assumption of the gradient Lipschitz continuity condition on the objective function to ensure overall convergence from the current knowledge. However, many practical applications do not adhere to the conditions of smoothness. In this study, we justify the convergence of variant Bregman ADMM for the problem with coupling terms to circumvent the issue of the global Lipschitz continuity of the gradient. We demonstrate that the iterative sequence generated by our approach converges to a critical point of the issue when the corresponding function fulfills the Kurdyka-Lojasiewicz inequality and certain assumptions apply. In addition, we illustrate the convergence rate of the algorithm.展开更多
This work investigated the applicability of heterogeneous and pseudo-homogeneous models to predict the dynamic behavior of a fixed-bed catalytic reactor. Some issues concerning the dynamic behavior of the system were ...This work investigated the applicability of heterogeneous and pseudo-homogeneous models to predict the dynamic behavior of a fixed-bed catalytic reactor. Some issues concerning the dynamic behavior of the system were discussed, such as the prediction of the inverse response phenomenon. The proposed models (Het- erogeneous I and II and Pseudo-homogeneous) were able to predict with qualitative similarity the main characteristics of the dynamic behavior of a fixed-bed catalytic reactor, including the inverse response. The computational time demanded for the solution of the heterogeneous models was 10 to 50% longer than in the case of the pseudo-homogeneous model, making the use of the former suitable for applications where computational time is not the major restriction (off-line applications). On the other hand, when on-line applications are required, the simplified model (Pseudo-homogeneous model) showed to be a good alternative because this model was able to predict (qualitatively) the dynamics of the reactor using a faster and easier numerical solution.展开更多
Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to b...Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to be recovered and z is the noise vector.Zhou and Yu[Front.Appl.Math.Stat.,5(2019),Article 14]recently proposed a novel non-convex weighted l_(r)-l_(2)minimization method for effective sparse recovery.In this paper,under newly coherence-based conditions,we study the non-convex weighted l_(r)-l_(2)minimization in reconstructing sparse signals that are contaminated by different noises.Concretely,the results reveal that if the coherenceμof measurement matrix A fulfillsμ<k(s;r,α,N),s>1,α^(1/r)N(1/2)<1,then any s-sparse signals in the noisy scenarios could be ensured to be reconstructed robustly by solving weighted l_(r)-l_(2)minimization non-convex optimization problem.Furthermore,some central remarks are presented to clear that the reconstruction assurance is much weaker than the existing ones.To the best of our knowledge,this is the first mutual coherence-based sufficient condition for such approach.展开更多
The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear dif...The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).展开更多
The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex...The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex programs.In this paper,we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints,where the dual variables are updated twice with different stepsizes.Under proper assumptions instead of the socalled Kurdyka-Lojasiewicz inequality,convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals,respectively.Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.展开更多
This paper investigates the problem of outlier-resistant distributed fusion filtering(DFF)for a class of multi-sensor nonlinear singular systems(MSNSSs)under a dynamic event-triggered scheme(DETS).To relieve the effec...This paper investigates the problem of outlier-resistant distributed fusion filtering(DFF)for a class of multi-sensor nonlinear singular systems(MSNSSs)under a dynamic event-triggered scheme(DETS).To relieve the effect of measurement outliers in data transmission,a self-adaptive saturation function is used.Moreover,to further reduce the energy consumption of each sensor node and improve the efficiency of resource utilization,a DETS is adopted to regulate the frequency of data transmission.For the addressed MSNSSs,our purpose is to construct the local outlier-resistant filter under the effects of the measurement outliers and the DETS;the local upper bound(UB)on the filtering error covariance(FEC)is derived by solving the difference equations and minimized by designing proper filter gains.Furthermore,according to the local filters and their UBs,a DFF algorithm is presented in terms of the inverse covariance intersection fusion rule.As such,the proposed DFF algorithm has the advantages of reducing the frequency of data transmission and the impact of measurement outliers,thereby improving the estimation performance.Moreover,the uniform boundedness of the filtering error is discussed and a corresponding sufficient condition is presented.Finally,the validity of the developed algorithm is checked using a simulation example.展开更多
This paper is concerned with the distributed resilient fusion filtering(DRFF)problem for a class of time-varying multi-sensor nonlinear stochastic systems(MNSSs)with random sensor delays(RSDs).The phenomenon of the RS...This paper is concerned with the distributed resilient fusion filtering(DRFF)problem for a class of time-varying multi-sensor nonlinear stochastic systems(MNSSs)with random sensor delays(RSDs).The phenomenon of the RSDs is modeled by a set of random variables with certain statistical features.In addition,the nonlinear function is handled via Taylor expansion in order to deal with the nonlinear fusion filtering problem.The aim of the addressed issue is to propose a DRFF scheme for MNSSs such that,for both RSDs and estimator gain perturbations,certain upper bounds of estimation error covariance(EEC)are given and locally minimized at every sample time.In the light of the obtained local filters,a new DRFF algorithm is developed via the matrix-weighted fusion method.Furthermore,a sufficient condition is presented,which can guarantee that the local upper bound of the EEC is bounded.Finally,a numerical example is provided,which can show the usefulness of the developed DRFF approach.展开更多
文摘Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.
文摘In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multipliers (ADMM), is employed to solve such problems typically, which still requires the assumption of the gradient Lipschitz continuity condition on the objective function to ensure overall convergence from the current knowledge. However, many practical applications do not adhere to the conditions of smoothness. In this study, we justify the convergence of variant Bregman ADMM for the problem with coupling terms to circumvent the issue of the global Lipschitz continuity of the gradient. We demonstrate that the iterative sequence generated by our approach converges to a critical point of the issue when the corresponding function fulfills the Kurdyka-Lojasiewicz inequality and certain assumptions apply. In addition, we illustrate the convergence rate of the algorithm.
文摘This work investigated the applicability of heterogeneous and pseudo-homogeneous models to predict the dynamic behavior of a fixed-bed catalytic reactor. Some issues concerning the dynamic behavior of the system were discussed, such as the prediction of the inverse response phenomenon. The proposed models (Het- erogeneous I and II and Pseudo-homogeneous) were able to predict with qualitative similarity the main characteristics of the dynamic behavior of a fixed-bed catalytic reactor, including the inverse response. The computational time demanded for the solution of the heterogeneous models was 10 to 50% longer than in the case of the pseudo-homogeneous model, making the use of the former suitable for applications where computational time is not the major restriction (off-line applications). On the other hand, when on-line applications are required, the simplified model (Pseudo-homogeneous model) showed to be a good alternative because this model was able to predict (qualitatively) the dynamics of the reactor using a faster and easier numerical solution.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12101454,12101512,12071380,62063031)by the Chongqing Normal University Foundation Project(Grant No.23XLB013)+8 种基金by the Fuxi Scientific Research Innovation Team of Tianshui Normal University(Grant No.FXD2020-03)by the National Natural Science Foundation of China(Grant No.12301594)by the China Postdoctoral Science Foundation(Grant No.2021M692681)by the Natural Science Foundation of Chongqing,China(Grant No.cstc2021jcyj-bshX0155)by the Fundamental Research Funds for the Central Universities(Grant No.SWU120078)by the Natural Science Foundation of Gansu Province(Grant No.21JR1RE292)by the College Teachers Innovation Foundation of Gansu Province(Grant No.2023B-132)by the Joint Funds of the Natural Science Innovation-driven development of Chongqing(Grant No.2023NSCQ-LZX0218)by the Chongqing Talent Project(Grant No.cstc2021ycjh-bgzxm0015).
文摘Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to be recovered and z is the noise vector.Zhou and Yu[Front.Appl.Math.Stat.,5(2019),Article 14]recently proposed a novel non-convex weighted l_(r)-l_(2)minimization method for effective sparse recovery.In this paper,under newly coherence-based conditions,we study the non-convex weighted l_(r)-l_(2)minimization in reconstructing sparse signals that are contaminated by different noises.Concretely,the results reveal that if the coherenceμof measurement matrix A fulfillsμ<k(s;r,α,N),s>1,α^(1/r)N(1/2)<1,then any s-sparse signals in the noisy scenarios could be ensured to be reconstructed robustly by solving weighted l_(r)-l_(2)minimization non-convex optimization problem.Furthermore,some central remarks are presented to clear that the reconstruction assurance is much weaker than the existing ones.To the best of our knowledge,this is the first mutual coherence-based sufficient condition for such approach.
基金NSF of Guangxi(Grant No.2023GXNSFAA026085)Guangxi Science and Technology Department Specific Research Project of Guangxi for Research Bases and Talents(Grant No.AD23023001)+1 种基金NNSF of China Grant Nos.12071413,12111530282 the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECHthe Innovation Project of Guangxi University for Nationalities(Grant No.gxun-chxps202072)。
文摘The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).
基金supported by the National Natural Science Foundation of China(Grant Nos.12001430,11801455,11971238)by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515012405)+4 种基金by the Shanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSQ001)by the Sichuan Science and Technology Program(Grant No.2023NSFSC1922)by the Innovation Team Funds of China West Normal University(Grant No.KCXTD2023-3)by the Fundamental Research Funds of China West Normal University(Grant No.23kc010)by the Open Project of Key Laboratory(Grant No.CSSXKFKTM202004),School of Mathematical Sciences,Chongqing Normal University.
文摘The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex programs.In this paper,we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints,where the dual variables are updated twice with different stepsizes.Under proper assumptions instead of the socalled Kurdyka-Lojasiewicz inequality,convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals,respectively.Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.
基金Project supported by the National Natural Science Foundation of China(No.12171124)the Natural Science Foundation of Heilongjiang Province of China(No.ZD2022F003)+1 种基金the National High-end Foreign Experts Recruitment Plan of China(No.G2023012004L)the Alexander von Humboldt Foundation of Germany。
文摘This paper investigates the problem of outlier-resistant distributed fusion filtering(DFF)for a class of multi-sensor nonlinear singular systems(MSNSSs)under a dynamic event-triggered scheme(DETS).To relieve the effect of measurement outliers in data transmission,a self-adaptive saturation function is used.Moreover,to further reduce the energy consumption of each sensor node and improve the efficiency of resource utilization,a DETS is adopted to regulate the frequency of data transmission.For the addressed MSNSSs,our purpose is to construct the local outlier-resistant filter under the effects of the measurement outliers and the DETS;the local upper bound(UB)on the filtering error covariance(FEC)is derived by solving the difference equations and minimized by designing proper filter gains.Furthermore,according to the local filters and their UBs,a DFF algorithm is presented in terms of the inverse covariance intersection fusion rule.As such,the proposed DFF algorithm has the advantages of reducing the frequency of data transmission and the impact of measurement outliers,thereby improving the estimation performance.Moreover,the uniform boundedness of the filtering error is discussed and a corresponding sufficient condition is presented.Finally,the validity of the developed algorithm is checked using a simulation example.
基金This work was supported in part by the National Natural Science Foundation of China under Grant Nos.12171124,61873058,and 61673141the Natural Science Foundation of Heilongjiang Province of China under Grant No.ZD2022F003+1 种基金the Key Foundation of Educational Science Planning in Heilongjiang Province of China under Grant No.GJB1422069the Alexander von Humboldt Foundation of Germany。
文摘This paper is concerned with the distributed resilient fusion filtering(DRFF)problem for a class of time-varying multi-sensor nonlinear stochastic systems(MNSSs)with random sensor delays(RSDs).The phenomenon of the RSDs is modeled by a set of random variables with certain statistical features.In addition,the nonlinear function is handled via Taylor expansion in order to deal with the nonlinear fusion filtering problem.The aim of the addressed issue is to propose a DRFF scheme for MNSSs such that,for both RSDs and estimator gain perturbations,certain upper bounds of estimation error covariance(EEC)are given and locally minimized at every sample time.In the light of the obtained local filters,a new DRFF algorithm is developed via the matrix-weighted fusion method.Furthermore,a sufficient condition is presented,which can guarantee that the local upper bound of the EEC is bounded.Finally,a numerical example is provided,which can show the usefulness of the developed DRFF approach.
