Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is prove

Komputasi Aliran Daya Optimal Sistem Tenaga Skala Besar Dengan Metode Primal Dual Interior Point

This paper focuses on the use of Primal Dual Interior Point method in the analysis of optimal power flow. Optimal power flow analysis with Primal Dual Interior Point method then compared with Linear Programming Method using Matpower program. The simulation results show that the computation results of Primal Dual Interior Point similar with Linear Programming Method for total cost of generation and large power generated by each power plant. But in terms of computation time Primal Dual Interior Point method is faster than the method of Linear Programming, especially for large systems. Primal Dual Interior Point method have solved the problem in 40.59 seconds, while Linear Programming method takes longer 239.72 seconds for large-scale system 9241 bus. This is because the settlement PDIP algorithm starts from the starting point x0, which is located within the area of feasible move towards the optimal point, in contrast to the simplex method that moves along the border of the feasible from one extreme point to the other extreme point. Thus Primal Dual Interior Point method have more efficient in solving optimal power flow problem of large-scale power systems

A Still Simpler Way of Introducing the Interior-Point Method for Linear Programming

Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical background of CS students. In particular, only limited knowledge of linear algebra and calculus is assumed.Comment: Updates and replaces arXiv:1412.065

Lineáris optimalizálás : elmélete és belsőpontos algoritmusai

Interior point methods for linear programming release the result of a long process. Today's knowledge, the first notable result was coined Frisch, who in 1955 gave a lecture at a seminar in the University of Oslo in the econometric seminar logarithmic barrier method of linear programming applicability. The method multiple algorithm called it, which was published in 1957. Another result that was almost unnoticed, Diki coined, and in 1967 was published. Diki introduced the ellipsoid named after him, which could help you to approach and approach to solve linear programming problems with a special structure. you define primal, affine scaling interior point algorithms using the method again

The implementation of interior-point method for solving nonlinear constrained optimization problems

In this research, we discuss linear and nonlinear programming problems and methods. We have implemented the simplex and interior-point methods for linear programming problems. We also implement interior-point method for nonlinear programming problems. The convergence analysis and complexity of these methods are presented. Computational results that compare between the simplex method and the interior-point method are reported