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Acta Mathematicae Applicatae Sinica 2019年第2期35卷 359-373页

作者： S.ASADI H.MANSOURI M.ZANGIABADI Department of Applied Mathematics Faculty of Mathematical SciencesShahrekord University

In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming problems, where the objective function is a convex quadratic function and the feasible set is the intersection of an affine subspace and a symmetric cone attached to a Euclidean Jordan algebra. The algorithm is based on the [13] broad class of commutative search directions for cone of semidefinite matrices, extended by [18] to arbitrary symmetric cones. Despite the fact that the neighborhood is wider, which allows the iterates move towards optimality with longer steps, the complexity iteration bound remains as the same result of Schmieta and Alizadeh for symmetric cone optimization problems.

关键词： interior-point method symmetric cone convex quadratic programming wide neighborhood commutative class directions complexity bound

A Modified Full-NT-Step Infeasible interior-point Algorithm for SDP Based on a Specific Kernel Function

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Journal of Harbin Institute of Technology(New Series) 2019年第2期26卷 41-47页

作者： Yadan Wang Hongwei Liu Zexian Liu Department of Mathematics Xidian University School of Mathematics and Computer Science Hezhou University

This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.

关键词： semidefinite programming infeasible interior-point methods full Nesterov-Todd steps kernel functions polynomial complexity

interior-point Methods Applied to the Predispatch Problem of a Hydroelectric System with Scheduled Line Manipulations

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American Journal of Operations Research 2012年第2期2卷 266-271页

作者： Silvia M. S. Carvalho Aurelio R. L. Oliveira University of Campinas Campinas Brazil

Transmission line manipulations in a power system are necessary for the execution of preventative or corrective main- tenance in a network, thus ensuring the stability of the system. In this study, primal-dual interior-point methods are used to minimize costs and losses in the generation and transmission of the predispatch active power flow in a hydroelectric system with previously scheduled line manipulations for preventative maintenance, over a period of twenty-four hours. The matrix structure of this problem and the modification that it imposes on the system is also broached in this study. From the computational standpoint, the effort required to solve a problem with or without line manipulations is similar, and the reasons for this are also discussed in this study. Computational results sustain our findings.

关键词： interior-point Methods Scheduled Line Manipulations Hydroelectric Systems The Brazilian Power System

A New Full-NT-Step Infeasible interior-point Algorithm for SDP Based on a Specific Kernel Function

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Applied Mathematics 2012年第9期3卷 1014-1022页

作者： Samir Bouali Samir Kabbaj Department of Mathematics and Informatics Faculty of Sciences University Ibn Tofail Kenitra Morocco

In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.

关键词： Semidefinite Programming Full Nesterov-Todd Steps Infeasible interior-point Methods Polynomial Complexity Kernel Functions

A NEW FRAMEWORK OF PRIMAL-DUAL INFEASIBLE interior-point METHOD FOR LINEAR PROGRAMMING

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1998年第2期7卷 183-194页

作者：林正华宋岱才刘庆怀

On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.

关键词： Linear programming infeasible interior-point method homotopy method global convergence.

A PREDICTOR-CORRECTOR interior-point ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2002年第1期11卷 52-62页

作者： Liang Ximing(梁昔明) Qian Jixin(钱积新) College of Information Science ＆ Engineering Central South University Changsha 410083 Institute of Systems Engineering National Lab of Industrial Control Technology Zhejiang University Hangzhou 310027

The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.

关键词： convex quadratic programming, interior-point methods, predictor-corrector algorithms, numerical experiments.

An Improved Affine-Scaling interior point Algorithm for Linear Programming

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Journal of Applied Mathematics and Physics 2019年第10期7卷 2531-2536页

作者： Douglas Kwasi Boah Stephen Boakye Twum Department of Mathematics Faculty of Mathematical Sciences University for Development Studies Navrongo Ghana

In this paper, an Improved Affine-Scaling interior point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling interior point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.

关键词： interior-point Methods Affine-Scaling interior point Algorithm Optimal Solution Linear Programming Initial Feasible Trial Solution

Power System Reactive Power Optimization Based on Fuzzy Formulation and interior point Filter Algorithm

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Energy and Power Engineering 2013年第4期5卷 693-697页

作者： Zheng Fan Wei Wang Tian-jiao Pu Guang-yi Liu Zhi Cai Ning Yang China Electric Power Research Institute Beijing China Gansu Electric Power Corporation Lanzhou China Northeast China Grid Company Shenyang China

Considering the soft constraint characteristics of voltage constraints, the interior-point Filter Algorithm is applied to solve the formulation of fuzzy model for the power system reactive power optimization with a large number of equality and inequality constraints. Based on the primal-dual interior-point algorithm, the algorithm maintains an updating “filter” at each iteration in order to decide whether to admit correction of iteration point which can avoid effectively oscillation due to the conflict between the decrease of objective function and the satisfaction of constraints and ensure the global convergence. Moreover, the “filter” improves computational efficiency because it filters the unnecessary iteration points. The calculation results of a practical power system indicate that the algorithm can effectively deal with the large number of inequality constraints of the fuzzy model of reactive power optimization and satisfy the requirement of online calculation which realizes to decrease the network loss and maintain specified margins of voltage.

关键词： Power System Reactive Power Optimization Fuzzy Filter interior-point Algorithm Online Calculation

A New Prodictor-Corrector Path Following Method for Linear Programming

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湖北文理学院学报 1998年第2期31卷 2-8页

作者： Huang Zhenghai Wang Xianjie 襄阳师范高等专科学校物理系 441053

Based on wide-neighbourhood , we in this paper produce aprodictor-corrector algorithm for linear programming, which possesse onepredictor step and two corrector steps. Its iteration complixity bound isO(n2/3 L).Our algorithm improve on the iteration complexity of O(n3/4 L) ofthe predictor-corrector algorithm proposed by *** and ***.

关键词： interior-point algorithm prodictor-corrector algorithm

Predispatch of Hydroelectric Power Systems with Modifications in Network Topologies

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Applied Mathematics 2014年第15期5卷 2271-2283页

作者： Silvia M. S. Carvalho Aurelio Oliveira Federal University of Sao Carlos Sao Carlos Brazil University of Campinas Campinas Brazil

In this article, the primal-dual interior-point methods are used to minimize costs and losses in a predispatch model for the generation and transmission of direct current (DC) power flow in a hydroelectric system with pre-programmed manipulations;i.e., in cases of preventive maintenance, within a period of twenty-four hours. From the computational standpoint, the effort required to solve a problem with and without manipulations is similar, and the reasons why will be also discussed in this study. Computational results prove these findings.

关键词： Predispatch of Hydroelectric Systems interior-point Methods Hydroelectric Systems Power Systems