In this paper,an Unmanned Aerial Vehicle(UAV)-assisted relay communication system is studied,where a UAV is served as a flying relay to maintain a communication link between a mobile source node and a remote destinati...In this paper,an Unmanned Aerial Vehicle(UAV)-assisted relay communication system is studied,where a UAV is served as a flying relay to maintain a communication link between a mobile source node and a remote destination node.Specifically,an average outage probability minimization problem is formulated firstly,with the constraints on the transmission power of the source node,the maximum energy consumption budget,the transmission power,the speed and acceleration of the flying UAV relay.Next,the closed-form of outage probability is derived,under the hybrid line-of-sight and non-line-of-sight probability channel model.To deal with the formulated nonconvex optimization,a long-term proactive optimization mechanism is developed.In particular,firstly,an approximation for line-of-sight probability and a reformulation of the primal problem are given,respectively.Then,the reformulated problem is transformed into two subproblems:one is the transmission power optimization with given UAV’s trajectory and the other is the trajectory optimization with given transmission power allocation.Next,two subproblems are tackled via tailoring primal–dual subgradient method and successive convex approximation,respectively.Furthermore,a proactive optimization algorithm is proposed to jointly optimize the transmission power allocation and the three-dimensional trajectory.Finally,simulation results demonstrate the performance of the proposed algorithm under various parameter configurations.展开更多
A Lagrangian relaxation(LR) approach was presented which is with machine capacity relaxation and operation precedence relaxation for solving a flexible job shop(FJS) scheduling problem from the steelmaking-refining-co...A Lagrangian relaxation(LR) approach was presented which is with machine capacity relaxation and operation precedence relaxation for solving a flexible job shop(FJS) scheduling problem from the steelmaking-refining-continuous casting process. Unlike the full optimization of LR problems in traditional LR approaches, the machine capacity relaxation is optimized asymptotically, while the precedence relaxation is optimized approximately due to the NP-hard nature of its LR problem. Because the standard subgradient algorithm(SSA) cannot solve the Lagrangian dual(LD) problem within the partial optimization of LR problem, an effective deflected-conditional approximate subgradient level algorithm(DCASLA) was developed, named as Lagrangian relaxation level approach. The efficiency of the DCASLA is enhanced by a deflected-conditional epsilon-subgradient to weaken the possible zigzagging phenomena. Computational results and comparisons show that the proposed methods improve significantly the efficiency of the LR approach and the DCASLA adopting capacity relaxation strategy performs best among eight methods in terms of solution quality and running time.展开更多
This paper developed the dynamic feedback neural network model to solve the convex nonlinear programming problem proposed by Leung et al. and introduced subgradient-based dynamic feedback neural networks to solve non-...This paper developed the dynamic feedback neural network model to solve the convex nonlinear programming problem proposed by Leung et al. and introduced subgradient-based dynamic feedback neural networks to solve non-differentiable convex optimization problems. For unconstrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive, we proved that with arbitrarily given initial value, the trajectory of the feedback neural network constructed by a projection subgradient converges to an asymptotically stable equilibrium point which is also an optimal solution of the primal unconstrained problem. For constrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive and the constraint functions are convex also, the energy functions sequence and corresponding dynamic feedback subneural network models based on a projection subgradient are successively constructed respectively, the convergence theorem is then obtained and the stopping condition is given. Furthermore, the effective algorithms are designed and some simulation experiments are illustrated.展开更多
In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient ext...In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.展开更多
This paper studies the optimization problem of heterogeneous networks under a timevarying topology.Each agent only accesses to one local objective function,which is nonsmooth.An improved algorithm with noisy measureme...This paper studies the optimization problem of heterogeneous networks under a timevarying topology.Each agent only accesses to one local objective function,which is nonsmooth.An improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all agents.To weaken the effect of these noises,two step sizes are introduced in the control protocol.By graph theory,stochastic analysis and martingale convergence theory,it is proved that if the sub-gradients are uniformly bounded,the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected,then the designed control protocol can force all agents to find the global optimal point almost surely.At last,the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.展开更多
The subgradient, under the weak Benson proper efficiency, of a set-valued mapping in ordered Banach space is developed, and the weak Benson proper efficient Hahn-Banach theorem of a set-valued mapping is established, ...The subgradient, under the weak Benson proper efficiency, of a set-valued mapping in ordered Banach space is developed, and the weak Benson proper efficient Hahn-Banach theorem of a set-valued mapping is established, with which the existence of the subgradient is proved and the characterizations of weak Benson proper efficient elements of constrained(unconstrained) vector set-valued optimization problems are presented.展开更多
This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to ...This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.展开更多
Backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involve...Backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involved with such complex nonlinearities. In this paper, a nonsmooth recursive identification algorithm for the systems with backlash-like hysteresis is proposed. In this method, the concept of Clarke subgradient is introduced to approximate the gradients at nonsmooth points and the so-called bundle method is used to obtain the optimization search direction in nonsmooth cases. Then, a recursive algorithm based on the idea of bundle method is developed for parameter estimation. After that, the convergence analysis of the algorithm is investigated. Finally, simulation results to validate the proposed method on a simulated mechanical transmission system are presented.展开更多
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
基金co-supported by the Natural Science Foundation for Distinguished Young Scholars of Jiangsu Province(No.BK20190030)the National Natural Science Foundation of China(Nos.61871398 and 61931011)the National Key R&D Program of China(No.2018YFB1801103)。
文摘In this paper,an Unmanned Aerial Vehicle(UAV)-assisted relay communication system is studied,where a UAV is served as a flying relay to maintain a communication link between a mobile source node and a remote destination node.Specifically,an average outage probability minimization problem is formulated firstly,with the constraints on the transmission power of the source node,the maximum energy consumption budget,the transmission power,the speed and acceleration of the flying UAV relay.Next,the closed-form of outage probability is derived,under the hybrid line-of-sight and non-line-of-sight probability channel model.To deal with the formulated nonconvex optimization,a long-term proactive optimization mechanism is developed.In particular,firstly,an approximation for line-of-sight probability and a reformulation of the primal problem are given,respectively.Then,the reformulated problem is transformed into two subproblems:one is the transmission power optimization with given UAV’s trajectory and the other is the trajectory optimization with given transmission power allocation.Next,two subproblems are tackled via tailoring primal–dual subgradient method and successive convex approximation,respectively.Furthermore,a proactive optimization algorithm is proposed to jointly optimize the transmission power allocation and the three-dimensional trajectory.Finally,simulation results demonstrate the performance of the proposed algorithm under various parameter configurations.
基金Projects(51435009,51575212,61573249,61371200)supported by the National Natural Science Foundation of ChinaProjects(2015T80798,2014M552040,2014M561250,2015M571328)supported by Postdoctoral Science Foundation of ChinaProject(L2015372)supported by Liaoning Province Education Administration,China
文摘A Lagrangian relaxation(LR) approach was presented which is with machine capacity relaxation and operation precedence relaxation for solving a flexible job shop(FJS) scheduling problem from the steelmaking-refining-continuous casting process. Unlike the full optimization of LR problems in traditional LR approaches, the machine capacity relaxation is optimized asymptotically, while the precedence relaxation is optimized approximately due to the NP-hard nature of its LR problem. Because the standard subgradient algorithm(SSA) cannot solve the Lagrangian dual(LD) problem within the partial optimization of LR problem, an effective deflected-conditional approximate subgradient level algorithm(DCASLA) was developed, named as Lagrangian relaxation level approach. The efficiency of the DCASLA is enhanced by a deflected-conditional epsilon-subgradient to weaken the possible zigzagging phenomena. Computational results and comparisons show that the proposed methods improve significantly the efficiency of the LR approach and the DCASLA adopting capacity relaxation strategy performs best among eight methods in terms of solution quality and running time.
基金the National 973 Project （Grant No. 2002cb312205） the National Natural Science Foundation of China （Grant No. 60574077）.
文摘This paper developed the dynamic feedback neural network model to solve the convex nonlinear programming problem proposed by Leung et al. and introduced subgradient-based dynamic feedback neural networks to solve non-differentiable convex optimization problems. For unconstrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive, we proved that with arbitrarily given initial value, the trajectory of the feedback neural network constructed by a projection subgradient converges to an asymptotically stable equilibrium point which is also an optimal solution of the primal unconstrained problem. For constrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive and the constraint functions are convex also, the energy functions sequence and corresponding dynamic feedback subneural network models based on a projection subgradient are successively constructed respectively, the convergence theorem is then obtained and the stopping condition is given. Furthermore, the effective algorithms are designed and some simulation experiments are illustrated.
基金funded by the University of Science,Vietnam National University,Hanoi under project number TN.21.01。
文摘In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.
基金supported by the National Natural Science Foundation of China under Grant No.61973329National Key Technology R&D Program of China under Grant No.2021YFD2100605Project of Beijing Municipal University Teacher Team Construction Support Plan under Grant No.BPHR20220104。
文摘This paper studies the optimization problem of heterogeneous networks under a timevarying topology.Each agent only accesses to one local objective function,which is nonsmooth.An improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all agents.To weaken the effect of these noises,two step sizes are introduced in the control protocol.By graph theory,stochastic analysis and martingale convergence theory,it is proved that if the sub-gradients are uniformly bounded,the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected,then the designed control protocol can force all agents to find the global optimal point almost surely.At last,the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.
基金supported by National Science Foundation of China(under grant:10671126)Shanghai leading academic discipline project(under grant:S30501)+2 种基金the Innovation Fund Project for Graduate Student of Shanghai(JWCXSL1001)Youth Foundation of Henan Polytechnic University(Q2009-3)Applied Mathematics Provincial-level Key Discipline of Henan Province,Operations Research and Control Theory Key Discipline of Henan Polytechnic Univrsity
基金This research is supportedby the National Natural Science Foundation of China(69972036), the Natural Science Foundation of Shaan
文摘The subgradient, under the weak Benson proper efficiency, of a set-valued mapping in ordered Banach space is developed, and the weak Benson proper efficient Hahn-Banach theorem of a set-valued mapping is established, with which the existence of the subgradient is proved and the characterizations of weak Benson proper efficient elements of constrained(unconstrained) vector set-valued optimization problems are presented.
基金Supported by Natural Science Foundation of Shanghai(14ZR1429200)National Science Foundation of China(11171221)+4 种基金Shanghai Leading Academic Discipline Project(XTKX2012)Innovation Program of Shanghai Municipal Education Commission(14YZ094)Doctoral Program Foundation of Institutions of Higher Educationof China(20123120110004)Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002)Young Teacher Training Projection Program of Shanghai for Science and Technology
文摘This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.
基金supported by the National Natural Science Foundation of China (Nos. 61203108, 60971004, 61171088)the projects of the Science and Technology Commission of Shanghai (Nos. 09220503000, 10JC1412200, 09ZR1423400)the projects of Shanghai Education Commission(Nos. 11YZ92, 13YZ056)
文摘Backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involved with such complex nonlinearities. In this paper, a nonsmooth recursive identification algorithm for the systems with backlash-like hysteresis is proposed. In this method, the concept of Clarke subgradient is introduced to approximate the gradients at nonsmooth points and the so-called bundle method is used to obtain the optimization search direction in nonsmooth cases. Then, a recursive algorithm based on the idea of bundle method is developed for parameter estimation. After that, the convergence analysis of the algorithm is investigated. Finally, simulation results to validate the proposed method on a simulated mechanical transmission system are presented.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
