Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a noncon...Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints.展开更多
The increasing number of gas-fired units has significantly intensified the coupling between electric and gas power networks.Traditionally,nonlinearity and nonconvexity in gas flow equations,together with renewable-ind...The increasing number of gas-fired units has significantly intensified the coupling between electric and gas power networks.Traditionally,nonlinearity and nonconvexity in gas flow equations,together with renewable-induced stochasticity,resulted in a computationally expensive model for unit commitment in electricity-gas coupled integrated energy systems(IES).To accelerate stochastic day-ahead scheduling,we applied and modified Progressive Hedging(PH),a heuristic approach that can be computed in parallel to yield scenario-independent unit commitment.Through early termination and enumeration techniques,the modified PH algorithm saves considerable com,putational time for certain generation cost settings or when the scale of the IES is large.Moreover,an adapted second-order cone relaxation(SOCR)is utilized to tackle the nonconvex gas flow equation.Case studies were performed on the IEEE 24.bus system/Belgium 20-node gas system and the IEEE 118-bus system/Belgium 20-node gas system.The computational efficiency when employing PH is 188 times that of commercial software,and the algorithm even outperforms Benders Decomposition.At the same time,the gap between the PH algorithm and the benchmark is less than 0.01% in both IES systems,which proves that the solutions produced by PH reach acceptable optimality in this stochastic UC problem.展开更多
In this paper,we mainly study the existence of solutions to sparsity constrained optimization(SCO).Based on the expressions of tangent cone and normal cone of sparsity constraint,we present and characterize two first-...In this paper,we mainly study the existence of solutions to sparsity constrained optimization(SCO).Based on the expressions of tangent cone and normal cone of sparsity constraint,we present and characterize two first-order necessary optimality conditions for SCO:N-stationarity and T-stationarity.Then we give the second-order necessary and sufficient optimality conditions for SCO.At last,we extend these results to SCO with nonnegative constraint.展开更多
基金supported by US Army Research Office Grant(No.W911NF-04-D-0003)by the North Carolina State University Edward P.Fitts Fellowship and by National Natural Science Foundation of China(No.11171177)。
文摘Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints.
基金supported by the National Key Research and Development Program(SQ 2020YFE0200400)the National Natural Science Foundation of China(No.52007123)the Science,Technology and Innovation Commission of Shenzhen Municipality(No.JCYJ 20170411152331932).
文摘The increasing number of gas-fired units has significantly intensified the coupling between electric and gas power networks.Traditionally,nonlinearity and nonconvexity in gas flow equations,together with renewable-induced stochasticity,resulted in a computationally expensive model for unit commitment in electricity-gas coupled integrated energy systems(IES).To accelerate stochastic day-ahead scheduling,we applied and modified Progressive Hedging(PH),a heuristic approach that can be computed in parallel to yield scenario-independent unit commitment.Through early termination and enumeration techniques,the modified PH algorithm saves considerable com,putational time for certain generation cost settings or when the scale of the IES is large.Moreover,an adapted second-order cone relaxation(SOCR)is utilized to tackle the nonconvex gas flow equation.Case studies were performed on the IEEE 24.bus system/Belgium 20-node gas system and the IEEE 118-bus system/Belgium 20-node gas system.The computational efficiency when employing PH is 188 times that of commercial software,and the algorithm even outperforms Benders Decomposition.At the same time,the gap between the PH algorithm and the benchmark is less than 0.01% in both IES systems,which proves that the solutions produced by PH reach acceptable optimality in this stochastic UC problem.
基金supported in part by the National Natural Science Foundation of China(Nos.11431002,71271021).
文摘In this paper,we mainly study the existence of solutions to sparsity constrained optimization(SCO).Based on the expressions of tangent cone and normal cone of sparsity constraint,we present and characterize two first-order necessary optimality conditions for SCO:N-stationarity and T-stationarity.Then we give the second-order necessary and sufficient optimality conditions for SCO.At last,we extend these results to SCO with nonnegative constraint.
