A debris flow descending through an erodible convex colluvial bed,originating from a landslide dam and its upstream deposits,can entrain massive amounts of sediment,dramatically increasing the debris flow volume.Most ...A debris flow descending through an erodible convex colluvial bed,originating from a landslide dam and its upstream deposits,can entrain massive amounts of sediment,dramatically increasing the debris flow volume.Most existing erosion models assume that bed sediments are fully saturated,although this condition is rarely observed in nature.Therefore,a thorough understanding of debris flow overtopping erosion on a convex unsaturated bed is crucial for quantifying disaster risk.In this study,we experimentally investigated the effects of sediment composition,specifically coarse-grain size distribution and fine particle content,on the pore pressure evolution and entrainment of debris flows overriding a convex unsaturated colluvial bed.The average entrainment rate at convex sites for continuously graded bed sediment was higher than its discontinuous counterpart.The measured pore pressures within the unsaturated bed sediments were primarily generated by the passing debris flows.Furthermore,it was found that these pressures decreased as the fine particle content increased and the coarse-grain size of the erodible substrates decreased.When the coarse-grain size of the debris flow was smaller than that of the bed sediment,only a portion of the eroded material was entrained by the moving debris flow.In contrast,when the coarse-grain size of the debris flow was equal to or greater than that of the bed sediment,nearly all of the eroded material was entrained.The findings of this study could contribute to the assessment of hazard amplification and inform the design of mitigation and prevention strategies.展开更多
Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recov...Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.展开更多
Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequent...Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.展开更多
In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with lin...In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.展开更多
In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon....In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.展开更多
An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,...An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.展开更多
In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimat...In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in （in are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings （include quasi-convex mappings of type A and quasi-convex mappings of type B） in several complex variables are get accordingly. Our results state that a weak version of the Bieber- bach conjecture for quasi-convex mappings of type B and order a in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable.展开更多
In this paper,we define GG-E-convexity and GG-E-concavity.We also establish some inequalities in relation to GG-E-convex function using various integral inequalities with enough examples of various categories,which ve...In this paper,we define GG-E-convexity and GG-E-concavity.We also establish some inequalities in relation to GG-E-convex function using various integral inequalities with enough examples of various categories,which verifies our results.展开更多
Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient c...Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.展开更多
The hydrodynamic response of overland flow to vegetation coverage on convex slopes remains inadequately quantified despite it is critical for soil erosion control in terrains dominated by such topography.This study sy...The hydrodynamic response of overland flow to vegetation coverage on convex slopes remains inadequately quantified despite it is critical for soil erosion control in terrains dominated by such topography.This study systematically investigated the influence of varying vegetation coverage(0%,1.08%,3.24%,4.69%and 9.81%)on the hydrodynamic characteristics of convex slopes through indoor flume experiments under diverse flow discharges(5.5-13.5 m^(3)/h)and slopes(5°-25°).The results revealed three key hydrodynamic mechanisms:(1)Flow retardation and energy dissipation:Increasing vegetation coverage significantly reduced overland flow velocity and promoted higher flow depth,thereby enhancing water retention and energy dissipation.Both stream power(Ω)and unit stream power(ω)declined by 13.9%-30.1%compared to bare slopes.(2)Flow Regime Transition:Froude number(Fr)decreased with increasing vegetation coverage,promoting the transition from supercritical to subcritical flow.The Reynolds number(Re)consistently exceeded 500,indicating the absence of laminar flow.(3)Modification of flow resistance:Vegetation resistance increased nonlinearly with coverage.Maximum bed shear stress was observed at 4.69%coverage(23.5%higher than bare slopes).However,Manning’s(n)and Darcy-Weisbach(f)coefficients did not correlate clearly with Re,indicating that vegetation coverage and slope type feedback significantly change flow resistance mechanisms.展开更多
Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In t...Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In this paper,we embark on an in-depth exploration of the use of a quantum state prepared by the convex combination of given qubit states to optimally approximate the l_(1)-norm of coherence of the target quantum state,striving to make the prepared state and the target state as similar as possible.Here,we present the analytical solution for the optimal distance for any N given quantum states.We find that the optimal approximation problem for any N>4 quantum states can be transformed into an optimal approximation problem for no more than four quantum states,which not only significantly streamlines the problem but also proves advantageous for laboratories in terms of material conservation.Ultimately,a one-to-one comparison between the analytical and numerical solutions verifies the effectiveness of our approach.展开更多
Dear Editor,SO(3)SO(3)This letter proposes a continuous-time semi-decentralized algorithm to minimize a sum of local cost functions on over a multi-agent network.Inspired by the distributed subgradient method in[1],th...Dear Editor,SO(3)SO(3)This letter proposes a continuous-time semi-decentralized algorithm to minimize a sum of local cost functions on over a multi-agent network.Inspired by the distributed subgradient method in[1],the algorithm combines a consensus protocol on with a local Riemannian gradient term,but the state of each agent evolves on the nonlinear manifold.In absence of global information for each node,a coordinator is introduced in the communication network to ensure that all agents achieve convergence with consensus.Resorting to Lyapunov approaches,it is shown that the proposed algorithm reaches an optimal solution.展开更多
In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkow...In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkowski,van der Waerden,Hadwiger,Swinnerton-Dyer,Watson,Levenshtein,Odlyzko,Sloane and Musin.In this paper,we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results,in particular for balls in dimensions three,four and eight.展开更多
Dear Editor,This letter proposes a convex optimization-based model predictive control(MPC)autonomous guidance method for the Mars ascent vehicle(MAV).We use the modified chebyshev-picard iteration(MCPI)to solve optimi...Dear Editor,This letter proposes a convex optimization-based model predictive control(MPC)autonomous guidance method for the Mars ascent vehicle(MAV).We use the modified chebyshev-picard iteration(MCPI)to solve optimization sub-problems within the MPC framework,eliminating the dynamic constraints in solving the optimal control problem and enhancing the convergence performance of the algorithm.Moreover,this method can repeatedly perform trajectory optimization calculations at a high frequency,achieving timely correction of the optimal control command.Numerical simulations demonstrate that the method can satisfy the requirements of rapid computation and reliability for the MAV system when considering uncertainties and perturbations.展开更多
This work presents a nonlinear integral-ameliorated model for handling dynamic optimization problems with affine constraints.They pose a challenge as their optimal solutions evolve with time.Traditional iteration-base...This work presents a nonlinear integral-ameliorated model for handling dynamic optimization problems with affine constraints.They pose a challenge as their optimal solutions evolve with time.Traditional iteration-based methods that exactly solve the problem at each time instant,fail to precisely and realtime track the solution due to computational and communication bottlenecks.Our model,through rigorous theoretical analyses,is able to reduce the optimality gap(i.e.,the difference between the model state and optimal solution)to zero in a finite time,and thus,track the solution online.Besides,perturbance is taken into account.We prove that under certain conditions,our model can totally tolerate an important kind of noise that we call“errorrelated noise”.In numerical experiments,compared with six existing methods,our model exhibits superior robustness when contaminated by the error-related noise.The key techniques in the model design involve employing the zeroing neural network to leverage time-derivative information,and introducing an integral term as well as the class C_(L)^(0)functions to enhance convergence and noise resistance.Finally,we establish a model-free control framework for a surgical manipulator with the remote-center-of-motion constraint and compare the performances of the framework based on different models in simulations.The results indicate that our model achieves the best performance among various models employed within the framework.展开更多
In this paper, we introduce and study some new classes of biconvex functions with respect to an arbitrary function and a bifunction, which are called the higher order strongly biconvex functions. These functions are n...In this paper, we introduce and study some new classes of biconvex functions with respect to an arbitrary function and a bifunction, which are called the higher order strongly biconvex functions. These functions are nonconvex functions and include the biconvex function, convex functions, and <i>k</i>-convex as special cases. We study some properties of the higher order strongly biconvex functions. Several parallelogram laws for inner product spaces are obtained as novel applications of the higher order strongly biconvex affine functions. It is shown that the minimum of generalized biconvex functions on the <i>k</i>-biconvex sets can be characterized by a class of equilibrium problems, which is called the higher order strongly biequilibrium problems. Using the auxiliary technique involving the Bregman functions, several new inertial type methods for solving the higher order strongly biequilibrium problem are suggested and investigated. Convergence analysis of the proposed methods is considered under suitable conditions. Several important special cases are obtained as novel applications of the derived results. Some open problems are also suggested for future research.展开更多
Let C＇（α,β） be the class of functions f（z） =analytic in D ={z： ｜z｜ 〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z...Let C＇（α,β） be the class of functions f（z） =analytic in D ={z： ｜z｜ 〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z）/g（z）＋1-2α）｜ 〈β for some α β （0 ≤ α〈1,0 〈 β 〈 1）. A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C＇（α ,β ）. The results extend the work of C. Selvaraj.展开更多
基金supported by the National Key R&D Program of China(Grant No.2018YFC1505205)the Science and Technology Research Program of the Institute of Mountain Hazards and Environment,Chinese Academy of Sciences(Grant No.IMHE-ZDRW-01)Sichuan Science and Technology Program(Grant No.2024NSFSC0781).
文摘A debris flow descending through an erodible convex colluvial bed,originating from a landslide dam and its upstream deposits,can entrain massive amounts of sediment,dramatically increasing the debris flow volume.Most existing erosion models assume that bed sediments are fully saturated,although this condition is rarely observed in nature.Therefore,a thorough understanding of debris flow overtopping erosion on a convex unsaturated bed is crucial for quantifying disaster risk.In this study,we experimentally investigated the effects of sediment composition,specifically coarse-grain size distribution and fine particle content,on the pore pressure evolution and entrainment of debris flows overriding a convex unsaturated colluvial bed.The average entrainment rate at convex sites for continuously graded bed sediment was higher than its discontinuous counterpart.The measured pore pressures within the unsaturated bed sediments were primarily generated by the passing debris flows.Furthermore,it was found that these pressures decreased as the fine particle content increased and the coarse-grain size of the erodible substrates decreased.When the coarse-grain size of the debris flow was smaller than that of the bed sediment,only a portion of the eroded material was entrained by the moving debris flow.In contrast,when the coarse-grain size of the debris flow was equal to or greater than that of the bed sediment,nearly all of the eroded material was entrained.The findings of this study could contribute to the assessment of hazard amplification and inform the design of mitigation and prevention strategies.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.
基金supported by the National Natural Science Foundation of China(No.62203256)。
文摘Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.
基金supported by the National Natural Science Foundation of China(12171106)the Guangxi Science and Technology Program(AD23023001)+4 种基金the Natural Science Foundation of Guangxi Province(2023GXNSFBA026029)the National Natural Science Foundation of China(12401403,12361063)the Research Project of Guangxi Minzu University(2022KJQD03)the Middle-aged and Young Teachers’Basic Ability Promotion Project of Guangxi Province(2023KY0168)the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(2022GXUNXSHQN04).
文摘In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.
文摘In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.
文摘An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
基金Supported by National Natural Science Foundation of China(11471111)Guangdong Natural Science Foundation(2014A030307016)
文摘In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in （in are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings （include quasi-convex mappings of type A and quasi-convex mappings of type B） in several complex variables are get accordingly. Our results state that a weak version of the Bieber- bach conjecture for quasi-convex mappings of type B and order a in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable.
文摘A survey of recent progress on the multiplicity and stability problems for closed characteristics on compact convex hypersurfaces in R^(2n) is given.
文摘In this paper,we define GG-E-convexity and GG-E-concavity.We also establish some inequalities in relation to GG-E-convex function using various integral inequalities with enough examples of various categories,which verifies our results.
基金supported by the project Disuguaglianze analitiche e geometriche,funded by the Gruppo per Analisi Matematica la Probabilitàe le loro Applicazioni.
文摘Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.
基金financially supported by the National Natural Science Foundation of China(Grant NO.52279056)Inner Mongolia open list project(Grant NO.2024JBGS0023)。
文摘The hydrodynamic response of overland flow to vegetation coverage on convex slopes remains inadequately quantified despite it is critical for soil erosion control in terrains dominated by such topography.This study systematically investigated the influence of varying vegetation coverage(0%,1.08%,3.24%,4.69%and 9.81%)on the hydrodynamic characteristics of convex slopes through indoor flume experiments under diverse flow discharges(5.5-13.5 m^(3)/h)and slopes(5°-25°).The results revealed three key hydrodynamic mechanisms:(1)Flow retardation and energy dissipation:Increasing vegetation coverage significantly reduced overland flow velocity and promoted higher flow depth,thereby enhancing water retention and energy dissipation.Both stream power(Ω)and unit stream power(ω)declined by 13.9%-30.1%compared to bare slopes.(2)Flow Regime Transition:Froude number(Fr)decreased with increasing vegetation coverage,promoting the transition from supercritical to subcritical flow.The Reynolds number(Re)consistently exceeded 500,indicating the absence of laminar flow.(3)Modification of flow resistance:Vegetation resistance increased nonlinearly with coverage.Maximum bed shear stress was observed at 4.69%coverage(23.5%higher than bare slopes).However,Manning’s(n)and Darcy-Weisbach(f)coefficients did not correlate clearly with Re,indicating that vegetation coverage and slope type feedback significantly change flow resistance mechanisms.
基金supported by the Fundamental Research Projects of Shanxi Province(Grant No.202203021222225)the National Natural Science Foundation of China(Grant Nos.12175029,12011530014,and 11775040)the Key Research and Development Project of Liaoning Province(Grant No.2020JH2/10500003).
文摘Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In this paper,we embark on an in-depth exploration of the use of a quantum state prepared by the convex combination of given qubit states to optimally approximate the l_(1)-norm of coherence of the target quantum state,striving to make the prepared state and the target state as similar as possible.Here,we present the analytical solution for the optimal distance for any N given quantum states.We find that the optimal approximation problem for any N>4 quantum states can be transformed into an optimal approximation problem for no more than four quantum states,which not only significantly streamlines the problem but also proves advantageous for laboratories in terms of material conservation.Ultimately,a one-to-one comparison between the analytical and numerical solutions verifies the effectiveness of our approach.
基金supported by the National Key Research and Development Program of China(2022YFA1004701)the National Natural Science Foundation of China(72271187,62373283)Shanghai Municipal Science and Technology Major(2021SHZDZX0100).
文摘Dear Editor,SO(3)SO(3)This letter proposes a continuous-time semi-decentralized algorithm to minimize a sum of local cost functions on over a multi-agent network.Inspired by the distributed subgradient method in[1],the algorithm combines a consensus protocol on with a local Riemannian gradient term,but the state of each agent evolves on the nonlinear manifold.In absence of global information for each node,a coordinator is introduced in the communication network to ensure that all agents achieve convergence with consensus.Resorting to Lyapunov approaches,it is shown that the proposed algorithm reaches an optimal solution.
基金supported by the National Natural Science Foundation of China(12226006,11921001)the Natural Key Research and Development Program of China(2018YFA0704701).
文摘In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkowski,van der Waerden,Hadwiger,Swinnerton-Dyer,Watson,Levenshtein,Odlyzko,Sloane and Musin.In this paper,we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results,in particular for balls in dimensions three,four and eight.
基金supported by the National Defense Basic Scientific Research Program(JCKY2021603B030)the National Natural Science Foundation of China(62273118,12150008)the Natural Science Foundation of Heilongjiang Province(LH2022F023).
文摘Dear Editor,This letter proposes a convex optimization-based model predictive control(MPC)autonomous guidance method for the Mars ascent vehicle(MAV).We use the modified chebyshev-picard iteration(MCPI)to solve optimization sub-problems within the MPC framework,eliminating the dynamic constraints in solving the optimal control problem and enhancing the convergence performance of the algorithm.Moreover,this method can repeatedly perform trajectory optimization calculations at a high frequency,achieving timely correction of the optimal control command.Numerical simulations demonstrate that the method can satisfy the requirements of rapid computation and reliability for the MAV system when considering uncertainties and perturbations.
基金supported by the National Natural Science Foundation of China(62376290).
文摘This work presents a nonlinear integral-ameliorated model for handling dynamic optimization problems with affine constraints.They pose a challenge as their optimal solutions evolve with time.Traditional iteration-based methods that exactly solve the problem at each time instant,fail to precisely and realtime track the solution due to computational and communication bottlenecks.Our model,through rigorous theoretical analyses,is able to reduce the optimality gap(i.e.,the difference between the model state and optimal solution)to zero in a finite time,and thus,track the solution online.Besides,perturbance is taken into account.We prove that under certain conditions,our model can totally tolerate an important kind of noise that we call“errorrelated noise”.In numerical experiments,compared with six existing methods,our model exhibits superior robustness when contaminated by the error-related noise.The key techniques in the model design involve employing the zeroing neural network to leverage time-derivative information,and introducing an integral term as well as the class C_(L)^(0)functions to enhance convergence and noise resistance.Finally,we establish a model-free control framework for a surgical manipulator with the remote-center-of-motion constraint and compare the performances of the framework based on different models in simulations.The results indicate that our model achieves the best performance among various models employed within the framework.
文摘In this paper, we introduce and study some new classes of biconvex functions with respect to an arbitrary function and a bifunction, which are called the higher order strongly biconvex functions. These functions are nonconvex functions and include the biconvex function, convex functions, and <i>k</i>-convex as special cases. We study some properties of the higher order strongly biconvex functions. Several parallelogram laws for inner product spaces are obtained as novel applications of the higher order strongly biconvex affine functions. It is shown that the minimum of generalized biconvex functions on the <i>k</i>-biconvex sets can be characterized by a class of equilibrium problems, which is called the higher order strongly biequilibrium problems. Using the auxiliary technique involving the Bregman functions, several new inertial type methods for solving the higher order strongly biequilibrium problem are suggested and investigated. Convergence analysis of the proposed methods is considered under suitable conditions. Several important special cases are obtained as novel applications of the derived results. Some open problems are also suggested for future research.
文摘Let C＇（α,β） be the class of functions f（z） =analytic in D ={z： ｜z｜ 〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z）/g（z）＋1-2α）｜ 〈β for some α β （0 ≤ α〈1,0 〈 β 〈 1）. A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C＇（α ,β ）. The results extend the work of C. Selvaraj.
