The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point wit...The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.展开更多
This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such ...This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.展开更多
This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P_*(κ) linear complementarity problem(LCP),which is an extension of the work by Roos(SIAM J.Optim.,2006,16(4):1110-1136).The ma...This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P_*(κ) linear complementarity problem(LCP),which is an extension of the work by Roos(SIAM J.Optim.,2006,16(4):1110-1136).The main iteration consists of a feasibility step and several centrality steps.The authors introduce a specific kernel function instead of the classic logarithmical barrier function to induce the feasibility step,so the analysis of the feasibility step is different from that of Roos' s.This kernel function has a finite value on the boundary.The result of iteration complexity coincides with the currently known best one for infeasible interior-point methods for P_*(κ) LCP.Some numerical results are reported as well.展开更多
文摘The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.
基金supported by the National Science Foundation of China under Grant No.11371253
文摘This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.
基金supported by the Natural Science Foundation of Hubei Province under Grant No.2008CDZ047
文摘This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P_*(κ) linear complementarity problem(LCP),which is an extension of the work by Roos(SIAM J.Optim.,2006,16(4):1110-1136).The main iteration consists of a feasibility step and several centrality steps.The authors introduce a specific kernel function instead of the classic logarithmical barrier function to induce the feasibility step,so the analysis of the feasibility step is different from that of Roos' s.This kernel function has a finite value on the boundary.The result of iteration complexity coincides with the currently known best one for infeasible interior-point methods for P_*(κ) LCP.Some numerical results are reported as well.
