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Behrouz Kheirfam - One of the best experts on this subject based on the ideXlab platform.
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A full-Newton step infeasible Interior-Point Method based on a trigonometric kernel function without centering steps
Numerical Algorithms, 2019Co-Authors: Behrouz Kheirfam, Masoumeh HaghighiAbstract:In this paper, a full-Newton step infeasible Interior-Point Method for solving linear optimization problems is presented. In each iteration, the algorithm uses only one so-called feasibility step and computes the feasibility search directions by using a trigonometric kernel function with a double barrier term. Convergence of the algorithm is proved and it is shown that the complexity bound of the algorithm matches the currently best known iteration bound for infeasible Interior-Point Methods. Finally, some numerical results are provided to illustrate the performance of the proposed algorithm.
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Complexity analysis of infeasible Interior-Point Method for semidefinite optimization based on a new trigonometric kernel function
Optimization Letters, 2019Co-Authors: Masoumeh Moslemi, Behrouz KheirfamAbstract:In this paper, a full Nesterov–Todd step infeasible Interior-Point Method for solving semidefinite optimization problems based on a new kernel function is analyzed. In each iteration, the algorithm involves a feasibility step and several centrality steps. The centrality step is focused on Nesterov–Todd search directions, while we used a kernel function with trigonometric barrier term to induce the feasibility step. The complexity result coincides with the best-known iteration bound for infeasible Interior-Point Methods.
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An infeasible full NT-step interior point Method for circular optimization
Numerical Algebra Control & Optimization, 2017Co-Authors: Behrouz Kheirfam, Guoqiang WangAbstract:In this paper, we design a primal-dual infeasible Interior-Point Method for circular optimization that uses only full Nesterov-Todd steps. Each main iteration of the algorithm consisted of one so-called feasibility step. Furthermore, giving a complexity analysis of the algorithm, we derive the currently best-known iteration bound for infeasible Interior-Point Methods.
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An improved and modified infeasible Interior-Point Method for symmetric optimization
Asian-European Journal of Mathematics, 2016Co-Authors: Behrouz KheirfamAbstract:In this paper an improved and modified version of full Nesterov–Todd step infeasible Interior-Point Methods for symmetric optimization published in [A new infeasible Interior-Point Method based on Darvay’s technique for symmetric optimization, Ann. Oper. Res. 211(1) (2013) 209–224; G. Gu, M. Zangiabadi and C. Roos, Full Nesterov–Todd step infeasible Interior-Point Method for symmetric optimization, European J. Oper. Res. 214(3) (2011) 473–484; Simplified analysis of a full Nesterov–Todd step infeasible Interior-Point Method for symmetric optimization, Asian-Eur. J. Math. 8(4) (2015) 1550071, 14 pp.] is considered. Each main iteration of our algorithm consisted of only a feasibility step, whereas in the earlier versions each iteration is composed of one feasibility step and several — at most three — centering steps. The algorithm finds an [Formula: see text]-solution of the underlying problem in polynomial-time and its iteration bound improves the earlier bounds factor from [Formula: see text] and [Formula: see text] to [Formula: see text]. Moreover, our Method unifies the analysis for linear optimization, second-order cone optimization and semidefinite optimization.
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An improved and modified infeasible Interior-Point Method for symmetric optimization
Asian-european Journal of Mathematics, 2016Co-Authors: Behrouz KheirfamAbstract:In this paper an improved and modified version of full Nesterov–Todd step infeasible Interior-Point Methods for symmetric optimization published in [A new infeasible Interior-Point Method based on Darvay’s technique for symmetric optimization, Ann. Oper. Res. 211(1) (2013) 209–224; G. Gu, M. Zangiabadi and C. Roos, Full Nesterov–Todd step infeasible Interior-Point Method for symmetric optimization, European J. Oper. Res. 214(3) (2011) 473–484; Simplified analysis of a full Nesterov–Todd step infeasible Interior-Point Method for symmetric optimization, Asian-Eur. J. Math. 8(4) (2015) 1550071, 14 pp.] is considered. Each main iteration of our algorithm consisted of only a feasibility step, whereas in the earlier versions each iteration is composed of one feasibility step and several — at most three — centering steps. The algorithm finds an ϵ-solution of the underlying problem in polynomial-time and its iteration bound improves the earlier bounds factor from 162 and 83 to 11. Moreover, our Method unifies the analysis for linear optimization, second-order cone optimization and semidefinite optimization.
Hao Xiao-qiang - One of the best experts on this subject based on the ideXlab platform.
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A Combination Strategy for Reactive Power Optimization Based on Predictor-Corrector Interior Point Method and Improved Genetic Algorithm
Power system technology, 2008Co-Authors: Hao Xiao-qiangAbstract:Based on predictor-corrector interior point Method (PCIPM) and improved genetic algorithm (IGA), a combination strategy for reactive power optimization is proposed, which divides reactive power optimization problem into two sub-problems, i.e., continuous optimization and discrete optimization, then PCIPM and IGA are used to solve them respectively.Because the regulation of generator voltage is the main reactive power optimization measure in actual power network, so at first the constraints of discrete variables are not taken into account and the continuous variables are optimized by PCIPM;then keeping continuous variables invariant, the discrete variables are optimized by IGA;and then the alternately solving processes are repeatedly performed until the difference of network loss variation between the adjacent continuous optimization stage and discrete optimization stage is less than the set value.The simulation results of IEEE 14-bus system, IEEE 30-bus system, IEEE 57-bus system and IEEE 118-bus system show that the proposed combination strategy is superior to other combination strategies in convergence and calculation efficiency.
Sun Weizhen - One of the best experts on this subject based on the ideXlab platform.
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A Robust WLAV State Estimation Based on Multiple Predictor-Corrector Interior Point Method
Power system technology, 2013Co-Authors: Sun WeizhenAbstract:In allusion to the defect that during the weighted least absolute squares(WLAV) state estimation based on predictor-corrector primal-dual interior point Method(PCPDIPM) it is possible the corrector direction possibly points to wrong direction,a multiple PCPDIPM based robust WLAV state estimation algorithm is proposed.On the basis of PCPDIPM,through multiple correction the proposed algorithm dynamically estimates the centrality parameter and by use of two-stage linear searching Method the optimal proportion of the corrector direction in the Newton direction is determined to ensure that the iteration points draw close to centrality parameter.Finally,the effectiveness of the proposed Method is verified by simulation results of IEEE 14-bus system and test results of a certain provincial power grid in China.The convergence speed and robustness of the proposed Method are much better than the weighted least square state estimation with the function of bad data identification.
S. Granville - One of the best experts on this subject based on the ideXlab platform.
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Optimal reactive dispatch through interior point Methods
IEEE Transactions on Power Systems, 1994Co-Authors: S. GranvilleAbstract:An implementation of an interior point Method to the optimal reactive dispatch problem is described. The interior point Method used is based on the primal-dual algorithm and the numerical results in large scale networks (1832 and 3467 bus systems) have shown that this technique can be very effective to some optimal power flow applications. >
K P Wong - One of the best experts on this subject based on the ideXlab platform.
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decomposition coordination interior point Method and its application to multi area optimal reactive power flow
International Journal of Electrical Power & Energy Systems, 2011Co-Authors: Wenyuan Li, C Y Chung, K P WongAbstract:Abstract A decomposition–coordination interior point Method (DIPM) is presented and applied to the multi-area optimal reactive power flow (ORPF) problem in this paper. In the Method, the area distributed ORPF problem is first formed by introducing duplicated border variables. Then the nonlinear primal dual interior point Method (IPM) is directly applied to the distributed ORPF problem in which a Newton system with border-matrix-blocks is formulated. Finally the overall ORPF problem is solved in decomposition iterations with the Newton system being decoupled. The proposed DIPM inherits the good performance of the traditional IPM with a feature appropriate for distributed calculations among multiple areas. It can be easily extended to other distributed optimization problems of power systems. Numeric results of five IEEE Test Systems are demonstrated and comparisons are made with those obtained using the traditional auxiliary problem principle (APP) Method. The results show that the DIPM for the multi-area OPRF problem requires less iterations and CPU time, has better stability in convergence, and reaches better optimality compared to the traditional auxiliary problem principle Method.
