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A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

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Journal of Computational mathematics 2024年第3期42卷 784-813页

作者： Bo Zhang Yuelin Gao xia Liu xiaoli Huang school of Civil and Hydraulic Engineering School of Mathematics and StatisticsNingxia UniversityYinchuan 750021China school of mathematics and Information Science North Minzu UniversityYinchuan 750021China ningxia Province Key Laboratory of Intelligent Information and Data Processing Yinchuan 750021China school of mathematics and statistics Ningxia UniversityYinchuan 750021China

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network ***,most of the solutions to such problems are often designed for their unique *** paper puts forward a new global optimization algorithm for solving the problem *** first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer ***,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative *** that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is ***,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

关键词： Global optimization Branch and bound Quadratic fractional programming Mixed integer programming

A LOW-REGULARITY FOURIER INTEGRATOR FOR THE DAVEY-STEWARTSON II SYSTEM WITH ALMOST MASS CONSERVATION

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Acta Mathematica Scientia 2024年第4期44卷 1536-1549页

作者： Cui ning Chenxi HAO Yaohong WANG school of Financial mathematics and statistics Guangdong University of FinanceGuangzhou 510521China Center for Applied mathematics Tianjin UniversityTianjin 300072China

In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>*** main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.

关键词： Davey-StewartsonⅡsystem low-regularity exponential integrator first order accuracy mass conservation

A dynamical neural network approach for distributionally robust chance-constrained Markov decision process

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Science China mathematics 2024年第6期67卷 1395-1418页

作者： Tian xia Jia Liu Zhiping Chen school of mathematics and statistics Xi’an Jiaotong UniversityXi’an710049China

In this paper,we study the distributionally robust joint chance-constrained Markov decision *** the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty *** cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization *** results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.

关键词： Markov decision process chance constraints distributionally robust optimization moment-based ambiguity set dynamical neural network

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A wealth distribution model with a non-Maxwellian collision kernel

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Chinese Physics B 2024年第7期33卷 224-231页

作者：孟俊周霞赖绍永 College of mathematics and statistics Kashi UniversityKashi 844006China College of mathematics and Physics Mianyang Teacher's CollegeMianyang 621000China school of mathematics Southwestern University of Finance and EconomicsChengdu 611130China

A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent *** collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.

关键词： kinetic theory non-Maxwellian collision kernel wealth distribution Pareto index

Reorientation and obstacle avoidance control of free-floating modular robots using sinusoidal oscillator

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Chinese Journal of Aeronautics 2024年第6期37卷 262-275页

作者： Zhiyuan YANG Mingzhu LAI Jian QI ning ZHAO Xin SUI Jie ZHAO Yanhe ZHU State Key Laboratory of Robotics and System Harbin Institute of TechnologyHarbin 150001China school of mathematics and statistics Hainan Normal UniversityHaikou 571158China

This paper presents that a serpentine curve-based controller can solve locomotion control problems for articulated space robots with extensive flight phases,such as obstacle avoidance during free floating or attitude adjustment before *** proposed algorithm achieves articulated robots to use closed paths in the joint space to accomplish the above *** snakes,which can shuttle through gaps and adjust their landing posture by swinging their body during gliding in jungle environments,inspired the design of two *** first maneuver generates a rotation of the system by varying the moment of inertia between the joints of the robot,with the magnitude of the net rotation depending on the controller *** maneuver can be repeated to allow the robot to reach arbitrary *** second maneuver involves periodic undulations,allowing the robot to avoid collisions when the trajectory of the global Center of Mass(CM)passes through the *** maneuvers are based on the improved serpenoid curve,which can adapt to redundant systems consisting of different numbers of ***,the simulation illustrates that combining the two maneuvers can help a free-floating chain-type robot traverse complex *** proposed algorithm can be used with similar articulated robot models.

关键词： Collision avoidance Modularrobots Reorientation Free-floating space robots Nonholonomic systems Biologically inspired controllers Serpenoid curve

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

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Communications on Applied mathematics and Computation 2024年第1期6卷 625-657页

作者： Ruihan Guo Yinhua xia school of mathematics and statistics Zhengzhou UniversityZhengzhou450001HenanChina school of Mathematical Sciences University of Science and Technology of ChinaHefei230026AnhuiChina

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two *** popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple *** resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher *** this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization *** novelty lies in how the decoupling and linear implicit properties are maintained to improve the *** the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and *** experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

关键词： Two-phase incompressible flows Fully-decoupled High-order accurate Linear implicit Spectral deferred correction method Local discontinuous Galerkin method

Multiplicity of solutions for the semilinear subelliptic Dirichlet problem

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Science China mathematics 2024年第3期67卷 475-504页

作者： Hua Chen Hong-Ge Chen Jin-ning Li Xin Liao school of mathematics and statistics Wuhan UniversityWuhan 430072China Wuhan Institute of Physics and mathematics Innovation Academy for Precision Measurement Science and TechnologyChinese Academy of SciencesWuhan 430071China

In this paper,we study the semilinear subelliptic equation{−△Xu=f(x,u)+g(x,u)inΩ,u=0 on∂Ω,where△X=−∑m i=1 Xi∗Xi is the self-adjoint Hormander operator associated with the vector fields X=(X_(1),X_(2),...,X_(m))satisfying the Hormander's condition,f(x,u)∈C(Ω×R),g(x,u)is a Carathéodory function onΩ×R,andΩis an open bounded domain in R~n with smooth *** the perturbation from the symmetry method with the approaches involving the eigenvalue estimate and the Morse index in estimating the minimax values,we obtain two kinds of existence results for multiple weak solutions to the problem ***,we discuss the difference between the eigenvalue estimate approach and the Morse index approach in degenerate *** with the classical elliptic cases,both approaches here have their own strengths in the degenerate *** new phenomenon implies that the results in general degenerate cases would be quite different from the situations in classical elliptic cases.

关键词： degenerate elliptic equations Hormander operators perturbation method Morse index

Dynamic analysis of a latent HIV infection model with CTL immune and antibody responses

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International Journal of Biomathematics 2024年第3期17卷 289-316页

作者： Zhiqi Zhang Yuming Chen xia Wang Libin Rong school of mathematics and statistics Xinyang Normal university XinyangHenan 464000P.R.China Department of mathematics Wilfrid Laurier university WaterlooONN2L 3C5Canada Department of mathematics university of Florida GainesvilleFL 32611USA

This paper develops a mathematical model to investigate the Human Immunodeficiency Virus(HIV)infection *** model includes two transmission modes(cell-to-cell and cell-free),two adaptive immune responses(cytotoxic T-lymphocyte(CTL)and antibody),a saturated CTL immune response,and latent HIV *** existence and local stability of equilibria are fully characterized by four reproduction *** sensitivity analyses,we assess the partial rank correlation coefficients of these reproduction numbers and identify that the infection rate via cell-to-cell transmission,the number of new viruses produced by each infected cell during its life cycle,the clearance rate of free virions,and immune parameters have the greatest impact on the reproduction ***,we compare the effects of immune stimulation and cell-to-cell spread on the model's *** findings highlight the significance of adaptive immune responses in increasing the population of uninfected cells and reducing the numbers of latent cells,infected cells,and ***,cell-to-cell transmission is identified as a facilitator of HIV *** analytical and numerical results presented in this study contribute to a better understanding of HIV dynamics and can potentially aid in improving HIV management strategies.

关键词： HIV infection cell-to-cell transmission adaptive immune response latent infection local stability

A Reliable Iteration Algorithm for One-Bit Compressive Sensing on the Unit Sphere

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 801-822页

作者： Yan-cheng LU ning BI An-hua WAN school of mathematics Sun Yat-sen UniversityGuangzhou 510275China

The one-bit compressed sensing problem is of fundamental importance in many areas,such as wireless communication,statistics,and so ***,the optimization of one-bit problem coustrained on the unit sphere lacks an algorithm with rigorous mathematical proof of convergence and *** this paper,an iteration algorithm is established based on difference-of-convex algorithm for the one-bit compressed sensing problem constrained on the unit sphere,with iterating formula■,where C is the convex cone generated by the one-bit measurements andη_(1)>η_(2)>1/*** new algorithm is proved to converge as long as the initial point is on the unit sphere and accords with the measurements,and the convergence to the global minimum point of the l_(1)norm is discussed.

关键词： one-bit compressed sensing difference of convex algorithm iteration algorithm ■1-minimization

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