To properly describe and solve complex decision problems,research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important.We establish in this paper different Lipschitz-ty...To properly describe and solve complex decision problems,research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important.We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints.The obtained results extend some existing results for continuous quadratic programs,and,more importantly,lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.展开更多
Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regressio...Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.展开更多
High-reliability double-sided ring collector systems have been widely implemented in offshore wind farms (OWFs).It is challenging to achieve a globally optimal network topology and a cable capacity rating for the OWF ...High-reliability double-sided ring collector systems have been widely implemented in offshore wind farms (OWFs).It is challenging to achieve a globally optimal network topology and a cable capacity rating for the OWF collector system (CS) simultaneously.This paper proposes an optimal collector system planning (CSP) method for OWF with double-sided ring topology based on bidirectional flow conservation method to minimize cable costs and total power losses.By analyzing the power flow direction after faults,all fault scenarios are summarized into two fault conditions.The bidirectional flow conservation method is developed to reveal the matching mechanism between different cable sequence positions and their optimal ratings,considering the minimal rating requirements.The complex high-dimensional CSP problem,which involves the coupling characteristics of different cable parameters and system power flows,is convexified by equivalent alternative methods into a mixed-integer quadratic programming (MIQP) to guarantee a global optimal solution within feasible computation time,improving the solvability and practicality.The effectiveness of the proposed optimal CSP method has been validated in MATLAB.展开更多
The electrical array reconfiguration(EAR)method has become a promising solution to enhance photovoltaic(PV)system performance under partial shading conditions.Existing studies focus on maximizing single-period PV gene...The electrical array reconfiguration(EAR)method has become a promising solution to enhance photovoltaic(PV)system performance under partial shading conditions.Existing studies focus on maximizing single-period PV generation but neglect the impact of power fluctuation on grid stability.To address this,we propose a multi-period EAR method for multi-PV systems considering net power fluctuation mitigation.First,we design a multi-period EAR model to maximize total revenue by balancing electricity sales and net power fluctuation penalties,formulated as a stochastic mixed-integer quadratic programming problem.The model incorporates constraints on the average number of switching actions per unit time to ensure practical implementation.Then,to handle the unpredictability of partial shading conditions,we develop a Lyapunov optimization-based online algorithm to decouple the time-coupling constraints involving state transitions.Additionally,we propose a reduced set of EAR strategies to improve the computational efficiency.Numerical studies demonstrate that the proposed method significantly reduces net power fluctuations in distribution networks with high PV penetration rate and enhances total revenue compared with conventional methods.展开更多
This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem,which can be formulated as a mixed-integer quadratic programming problem and pr...This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem,which can be formulated as a mixed-integer quadratic programming problem and proven to be NP-hard.Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided.Computational results support the effectiveness and efficiency of the proposed algorithm for solving large-scale problems.展开更多
基金Supported by the National Natural Science Foundation of China(10571141,70971109)the Key Projectof the National Natural Science Foundation of China(70531030)
文摘To properly describe and solve complex decision problems,research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important.We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints.The obtained results extend some existing results for continuous quadratic programs,and,more importantly,lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.
基金韩国国际合作项目(Development of Embedded Software and System for Automobile Electronics)重庆市科技攻关计划项目(CSTC+2 种基金2006AB2026)"面向汽车ABS嵌入式系统的专用开发平台及其应用"国家863计划项目(2006AA11A107-2)节能与新能源汽车-"长安混合动力汽车标定系统开发"国家863计划重点资助项目(2004AA1Z2380)"面向汽车电子控制的嵌入式系统开发平台及其应用"
基金supported by the National Natural Science Foundation of China grants(Nos.11101092,10971034)the Joint National Natural Science Foundation of China/Research Grants Council of Hong Kong grant(No.71061160506)the Research Grants Council of Hong Kong grants(Nos.CUHK414808 and CUHK414610).
文摘Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.
基金supported by the National Key R&D Program of China(No.2022YFF0608700)the National Natural Science Foundation of China(No.52207050)Basic Research Funds for Central Universities(No.531118010949).
文摘High-reliability double-sided ring collector systems have been widely implemented in offshore wind farms (OWFs).It is challenging to achieve a globally optimal network topology and a cable capacity rating for the OWF collector system (CS) simultaneously.This paper proposes an optimal collector system planning (CSP) method for OWF with double-sided ring topology based on bidirectional flow conservation method to minimize cable costs and total power losses.By analyzing the power flow direction after faults,all fault scenarios are summarized into two fault conditions.The bidirectional flow conservation method is developed to reveal the matching mechanism between different cable sequence positions and their optimal ratings,considering the minimal rating requirements.The complex high-dimensional CSP problem,which involves the coupling characteristics of different cable parameters and system power flows,is convexified by equivalent alternative methods into a mixed-integer quadratic programming (MIQP) to guarantee a global optimal solution within feasible computation time,improving the solvability and practicality.The effectiveness of the proposed optimal CSP method has been validated in MATLAB.
基金supported by the Shanghai Science and Technology Plan Project(No.23DZ1201200)National Natural Science Foundation of China(No.52477110).
文摘The electrical array reconfiguration(EAR)method has become a promising solution to enhance photovoltaic(PV)system performance under partial shading conditions.Existing studies focus on maximizing single-period PV generation but neglect the impact of power fluctuation on grid stability.To address this,we propose a multi-period EAR method for multi-PV systems considering net power fluctuation mitigation.First,we design a multi-period EAR model to maximize total revenue by balancing electricity sales and net power fluctuation penalties,formulated as a stochastic mixed-integer quadratic programming problem.The model incorporates constraints on the average number of switching actions per unit time to ensure practical implementation.Then,to handle the unpredictability of partial shading conditions,we develop a Lyapunov optimization-based online algorithm to decouple the time-coupling constraints involving state transitions.Additionally,we propose a reduced set of EAR strategies to improve the computational efficiency.Numerical studies demonstrate that the proposed method significantly reduces net power fluctuations in distribution networks with high PV penetration rate and enhances total revenue compared with conventional methods.
基金This work was supported by the National Natural Science Foundation of China(Nos.11771243,12171151,and 11701177)US Army Research Office(No.W911NF-15-1-0223).
文摘This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem,which can be formulated as a mixed-integer quadratic programming problem and proven to be NP-hard.Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided.Computational results support the effectiveness and efficiency of the proposed algorithm for solving large-scale problems.
