In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this mo...In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.展开更多
In this paper,the quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratic inequality constraints and entropy constraints of density are considered.Based on the properties...In this paper,the quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratic inequality constraints and entropy constraints of density are considered.Based on the properties of the generalized geometric programming,the dual programs of these two problems are derived.Furthermore,the duality theorems and related Kuhn-Tucker conditions for two pairs of the prime-dual programs are also established by the duality theory.展开更多
In this paper,on the basis of making full use of the characteristics of unconstrained generalized geometric programming（GGP）,we establish a nonmonotonic trust region algorithm via the conjugate path for solving unco...In this paper,on the basis of making full use of the characteristics of unconstrained generalized geometric programming（GGP）,we establish a nonmonotonic trust region algorithm via the conjugate path for solving unconstrained GGP problem.A new type of condensation problem is presented,then a particular conjugate path is constructed for the problem,along which we get the approximate solution of the problem by nonmonotonic trust region algorithm,and further prove that the algorithm has global convergence and quadratic convergence properties.展开更多
The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-o...The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.展开更多
This paper presents an efficient method for globally optimizing and automating component sizing for rotary traveling wave oscillator arrays. The lumped equivalent model of transmission lines loaded by inverter pairs i...This paper presents an efficient method for globally optimizing and automating component sizing for rotary traveling wave oscillator arrays. The lumped equivalent model of transmission lines loaded by inverter pairs is evaluated and posynomial functions for oscillation frequency, power dissipation, phase noise, etc. are formulated using transmission line theory. The re- sulting design problem can be posed as a geometric programJning problem, which can be efficiently solved with a convex opti- mization solver. The proposed method can compute the global optima more efficiently than the traditional iterative scheme and various design problems can be solved with the same circuit model. The globally optimal trade-off curves between competing objectives are also computed to carry out robust designs and quickly explore the design space.展开更多
This paper addresses a geometric programming problem,where the objective function and constraints are interval-valued functions.The concept of acceptable feasible region is introduced,and a methodology is developed t...This paper addresses a geometric programming problem,where the objective function and constraints are interval-valued functions.The concept of acceptable feasible region is introduced,and a methodology is developed to transform this model to a general optimization problem,which is free from interval uncertainty.Relationship between the solution of the original problem and the transformed problem is established.The methodology is illustrated through numerical examples.Solutions by the proposed method and previous methods are analyzed.展开更多
An optimization design technique to obtain global solution for a two-stage operational amplifier(op-amp) with frequency compensation is presented.This frequency compensation technique can adjust the equivalent resista...An optimization design technique to obtain global solution for a two-stage operational amplifier(op-amp) with frequency compensation is presented.This frequency compensation technique can adjust the equivalent resistance to guarantee that the phase margin is stable even though circumstance temperature varies.Geometric programming is used to optimize the component values and transistor dimensions.It is used in this analog integrated circuit design to calculate these parameters automatically.This globally optimal amplifier obtains minimum power while other specifications are fulfilled.展开更多
Sparse code multiple access (SCMA) is the most concerning scheme among non-orthogonal multiple access (NOMA) technologies for 5G wireless communication new interface. Another efficient technique in 5G aimed to improve...Sparse code multiple access (SCMA) is the most concerning scheme among non-orthogonal multiple access (NOMA) technologies for 5G wireless communication new interface. Another efficient technique in 5G aimed to improve spectral efficiency for local communications is device-to-device (D2D) communications. Therefore, we utilize the SCMA cellular network coexisting with D2D communications for the connection demand of the Internet of things (IOT), and improve the system sum rate performance of the hybrid network. We first derive the information-theoretic expression of the capacity for all users and find the capacity bound of cellular users based on the mutual interference between cellular users and D2D users. Then we consider the power optimization problem for the cellular users and D2D users jointly to maximize the system sum rate. To tackle the non-convex optimization problem, we propose a geometric programming (GP) based iterative power allocation algorithm. Simulation results demonstrate that the proposed algorithm converges fast and well improves the sum rate performance.展开更多
In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellu...In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.展开更多
Different schemes, which performed channel, power and time allocation to enhance the network performance of overall end-to-end throughput for cooperative cognitive radio network, were investigated. Interference temper...Different schemes, which performed channel, power and time allocation to enhance the network performance of overall end-to-end throughput for cooperative cognitive radio network, were investigated. Interference temperature limit of corresponding primary users was considered. Due to the constraints caused by multiple dual channels, the power allocation problem is non-convex and NP-hard. Based on geometric programming (GP), a novel and general algorithm, which turned the problem into a series of GP problems by logarithm approximation (LASGP), was proposed to efficiently solve it. Numerical results verify the efficiency and availability of the LASGP algorithm. Solutions of LASGP are provably convergent and globally optimal point can be observed as well as the channel allocation always outperforms power or timeslot allocation from simulations. Compared with schemes without any allocation, the scheme with joint channel, power and timeslot allocation significantly increases the overall end-to-end throughput by no less than 70% under same simulation conditions. This scheme can not only maximize the throughput by increasing total maximum power of relay node, but also outperform other resource allocation schemes when lower total maximum power of source and relay nodes is restricted. As the total maximum power of source node increases, the scheme with joint channel and timeslot allocation performs best in all schemes.展开更多
A Higgs-Yang-Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual α plane fields are holomorphic, but the right outgoing SD β plane fields are antiholomorphi...A Higgs-Yang-Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual α plane fields are holomorphic, but the right outgoing SD β plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse afiine rapidity parameters μ and μ^-1. The Dirac wave function scattering in this background also factorized respectively into the （anti）holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conformal affine massive field. We find explicit Nahm transformation matrix （Fourier Mukai transformation） between the Higgs YM BPS （fiat） bundles （1） modules） and the affinized blow up ADHMN twistors （perverse sheafs）. Thus we establish the algebra for the ＇t Hooft Hecke operators in the Hecke correspondence of the geometric Langlands program.展开更多
This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give...This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.展开更多
For a classical order quantity/pricing problem,we present a geometric programming(GP)approach to find the optimal selling price,order quantity and quality level to maximize the profit for the retail firm.Traditional m...For a classical order quantity/pricing problem,we present a geometric programming(GP)approach to find the optimal selling price,order quantity and quality level to maximize the profit for the retail firm.Traditional models such as EOQ are not able to handle the nonlinearity of costs and demand.We adopt the GP approach and make a proper transformation of the model so as to solve this classical problem and obtain the global optimal solution.In addition to the optimal solutions,we also perform a sensitivity analysis.The study shows once more that GP is an excellent approach when decision variables interact in a nonlinear,especially exponential manner.展开更多
A hybrid system of cellular mode and device-to-device （D2D） mode is considered in this paper, where the cellular resource is reused by the D2D transmission. With the objective of capacity maximization, the power opt...A hybrid system of cellular mode and device-to-device （D2D） mode is considered in this paper, where the cellular resource is reused by the D2D transmission. With the objective of capacity maximization, the power optimization of D2D sub-system is considered, taking into account quality of service （QoS） requirement. The power optimization problem is divided into two stages： The first stage is the admission control scheme design based on the QoS requirement of D2D users, and the second is power allocation to maximize aggregate throughput of admissible D2D users. For the D2D admission control problem, a heuristic sorting-based algorithm is proposed to index the admissible D2D links, where gain to Interference ratio （GIR） sorting criterion is used. Applying an approximate form of Shannon capacity, the power allocation problem can be solved by convex optimization and geometric programming tools efficiently. Based on the theoretical analysis, a practical algorithm is proposed. The precision can reach a trade-off between complexity and performance. Numerical simulation results confirm that combining with GIR sorting method, the proposed scheme can significantly improve the D2D system＇s capacity and fairness.展开更多
基金Supported by the NSF Jiangsu Province(BK2003211)Supported by the NSF of Henan Province(2003120001)
文摘In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.
文摘In this paper,the quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratic inequality constraints and entropy constraints of density are considered.Based on the properties of the generalized geometric programming,the dual programs of these two problems are derived.Furthermore,the duality theorems and related Kuhn-Tucker conditions for two pairs of the prime-dual programs are also established by the duality theory.
基金Supported by the National Science Foundation of China（10671126） Supported by the Shanghai Municipal Government Project（S30501）+3 种基金 Supported by the Innovation Fund Project for Graduate Student of Shanghai（JWCXSL1001） Supported by the Youth Foundation of Henan Polytechnic University（Q20093） Supported by the Applied Mathematics Provinciallevel Key Discipline of Henan Province Supported by Operational Research and Control Theory Key Discipline of Henan Polytechnic University
文摘In this paper,on the basis of making full use of the characteristics of unconstrained generalized geometric programming（GGP）,we establish a nonmonotonic trust region algorithm via the conjugate path for solving unconstrained GGP problem.A new type of condensation problem is presented,then a particular conjugate path is constructed for the problem,along which we get the approximate solution of the problem by nonmonotonic trust region algorithm,and further prove that the algorithm has global convergence and quadratic convergence properties.
文摘The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.
基金Project (No 20060335065) supported by the Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education, China
文摘This paper presents an efficient method for globally optimizing and automating component sizing for rotary traveling wave oscillator arrays. The lumped equivalent model of transmission lines loaded by inverter pairs is evaluated and posynomial functions for oscillation frequency, power dissipation, phase noise, etc. are formulated using transmission line theory. The re- sulting design problem can be posed as a geometric programJning problem, which can be efficiently solved with a convex opti- mization solver. The proposed method can compute the global optima more efficiently than the traditional iterative scheme and various design problems can be solved with the same circuit model. The globally optimal trade-off curves between competing objectives are also computed to carry out robust designs and quickly explore the design space.
文摘This paper addresses a geometric programming problem,where the objective function and constraints are interval-valued functions.The concept of acceptable feasible region is introduced,and a methodology is developed to transform this model to a general optimization problem,which is free from interval uncertainty.Relationship between the solution of the original problem and the transformed problem is established.The methodology is illustrated through numerical examples.Solutions by the proposed method and previous methods are analyzed.
基金the Shanghai Application Material(AM) Research Foundation (No.08700740700)
文摘An optimization design technique to obtain global solution for a two-stage operational amplifier(op-amp) with frequency compensation is presented.This frequency compensation technique can adjust the equivalent resistance to guarantee that the phase margin is stable even though circumstance temperature varies.Geometric programming is used to optimize the component values and transistor dimensions.It is used in this analog integrated circuit design to calculate these parameters automatically.This globally optimal amplifier obtains minimum power while other specifications are fulfilled.
基金supported by National key project 2018YFB1801102 and 2020YFB1807700by NSFC 62071296STCSM 20JC1416502, 22JC1404000
文摘Sparse code multiple access (SCMA) is the most concerning scheme among non-orthogonal multiple access (NOMA) technologies for 5G wireless communication new interface. Another efficient technique in 5G aimed to improve spectral efficiency for local communications is device-to-device (D2D) communications. Therefore, we utilize the SCMA cellular network coexisting with D2D communications for the connection demand of the Internet of things (IOT), and improve the system sum rate performance of the hybrid network. We first derive the information-theoretic expression of the capacity for all users and find the capacity bound of cellular users based on the mutual interference between cellular users and D2D users. Then we consider the power optimization problem for the cellular users and D2D users jointly to maximize the system sum rate. To tackle the non-convex optimization problem, we propose a geometric programming (GP) based iterative power allocation algorithm. Simulation results demonstrate that the proposed algorithm converges fast and well improves the sum rate performance.
基金supported by National Natural Science Foundation of China (No.61501028)Beijing Institute of Technology Research Fund Program for Young Scholars
文摘In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.
基金Project(60902092) supported by the National Natural Science Foundation of China
文摘Different schemes, which performed channel, power and time allocation to enhance the network performance of overall end-to-end throughput for cooperative cognitive radio network, were investigated. Interference temperature limit of corresponding primary users was considered. Due to the constraints caused by multiple dual channels, the power allocation problem is non-convex and NP-hard. Based on geometric programming (GP), a novel and general algorithm, which turned the problem into a series of GP problems by logarithm approximation (LASGP), was proposed to efficiently solve it. Numerical results verify the efficiency and availability of the LASGP algorithm. Solutions of LASGP are provably convergent and globally optimal point can be observed as well as the channel allocation always outperforms power or timeslot allocation from simulations. Compared with schemes without any allocation, the scheme with joint channel, power and timeslot allocation significantly increases the overall end-to-end throughput by no less than 70% under same simulation conditions. This scheme can not only maximize the throughput by increasing total maximum power of relay node, but also outperform other resource allocation schemes when lower total maximum power of source and relay nodes is restricted. As the total maximum power of source node increases, the scheme with joint channel and timeslot allocation performs best in all schemes.
基金National Natural Science Foundation of China under Grant No.90403019
文摘A Higgs-Yang-Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual α plane fields are holomorphic, but the right outgoing SD β plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse afiine rapidity parameters μ and μ^-1. The Dirac wave function scattering in this background also factorized respectively into the （anti）holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conformal affine massive field. We find explicit Nahm transformation matrix （Fourier Mukai transformation） between the Higgs YM BPS （fiat） bundles （1） modules） and the affinized blow up ADHMN twistors （perverse sheafs）. Thus we establish the algebra for the ＇t Hooft Hecke operators in the Hecke correspondence of the geometric Langlands program.
文摘This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.
基金This research is supported in part by National Science Foundation of China(Grant No.:71125003 and 71421002).
文摘For a classical order quantity/pricing problem,we present a geometric programming(GP)approach to find the optimal selling price,order quantity and quality level to maximize the profit for the retail firm.Traditional models such as EOQ are not able to handle the nonlinearity of costs and demand.We adopt the GP approach and make a proper transformation of the model so as to solve this classical problem and obtain the global optimal solution.In addition to the optimal solutions,we also perform a sensitivity analysis.The study shows once more that GP is an excellent approach when decision variables interact in a nonlinear,especially exponential manner.
基金sponsored by Renesas, the National Natural Science Foundation of China (60572120, 60602058)the National Basic Research Program of China (2009CB320400)+1 种基金the Joint Funds of NSFC-Guangdong (U1035001)the Chinese Major Science and Technology Projects (2009ZX03007-004)
文摘A hybrid system of cellular mode and device-to-device （D2D） mode is considered in this paper, where the cellular resource is reused by the D2D transmission. With the objective of capacity maximization, the power optimization of D2D sub-system is considered, taking into account quality of service （QoS） requirement. The power optimization problem is divided into two stages： The first stage is the admission control scheme design based on the QoS requirement of D2D users, and the second is power allocation to maximize aggregate throughput of admissible D2D users. For the D2D admission control problem, a heuristic sorting-based algorithm is proposed to index the admissible D2D links, where gain to Interference ratio （GIR） sorting criterion is used. Applying an approximate form of Shannon capacity, the power allocation problem can be solved by convex optimization and geometric programming tools efficiently. Based on the theoretical analysis, a practical algorithm is proposed. The precision can reach a trade-off between complexity and performance. Numerical simulation results confirm that combining with GIR sorting method, the proposed scheme can significantly improve the D2D system＇s capacity and fairness.
