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
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
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
In this paper,the growth theorem for convex maps on the Banach space is given, this is: ‖f(x)‖≤‖x‖/(1-‖x‖),x∈B the estimate is best possible for Hilbert space.
An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vert...An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.展开更多
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un...Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))...Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.展开更多
非相干多径弥散信道的特性和LED灯发射机的特性使得室内可见光通信系统难以提供室内均匀的通信性能。为了获得近似均匀的通信性能,提出了一种通过反向设计的基于Convex优化的灯排布方案。仿真结果显示,提出的灯排布方案使系统的接收光...非相干多径弥散信道的特性和LED灯发射机的特性使得室内可见光通信系统难以提供室内均匀的通信性能。为了获得近似均匀的通信性能,提出了一种通过反向设计的基于Convex优化的灯排布方案。仿真结果显示,提出的灯排布方案使系统的接收光功率波动从2.706 d B下降到0.277 d B,Q因子从3.224上升到36.271,并符合照明要求。展开更多
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.
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.
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.
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 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.
文摘In this paper,the growth theorem for convex maps on the Banach space is given, this is: ‖f(x)‖≤‖x‖/(1-‖x‖),x∈B the estimate is best possible for Hilbert space.
文摘An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.
文摘Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
文摘Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.
文摘非相干多径弥散信道的特性和LED灯发射机的特性使得室内可见光通信系统难以提供室内均匀的通信性能。为了获得近似均匀的通信性能,提出了一种通过反向设计的基于Convex优化的灯排布方案。仿真结果显示,提出的灯排布方案使系统的接收光功率波动从2.706 d B下降到0.277 d B,Q因子从3.224上升到36.271,并符合照明要求。
