Using the Interior Point Method to Find Normal Solutions to a System of Linear Algebraic Equations with Bilateral Constraints on Variables*
- 40 Downloads
The authors consider primal interior point algorithms to find normal solutions to systems of linear equations with bilateral constraints on variables. Analyzing this problem and the methods of its solution is important to develop the theory of mathematical modeling (in particular, to solve power engineering problems) and to create efficient computational algorithms. The paper contains the results of experimental analysis of the algorithms using test problems and identifies the ways to accelerate the computational process.
Keywordssystem of linear algebraic equations (SLAE) interior point algorithms normal solution bilateral constraints on variables
Unable to display preview. Download preview PDF.
- 1.P. I. Stetsyuk, E. A. Nurminskii, and D. I. Solomon, “Transportation problem and orthogonal projection onto linear manifolds,” in: Proc. 5th Intern. Sci. Conf. Transportation Systems and Logistics, Kishineu, December 11–13, 2013, Eureka, Kishineu (2013), pp. 251–263.Google Scholar
- 2.A. Yu. Filatov, Development of Interior Point Algorithms and their Applications to Systems of Inequalities, Author’s Abstracts of PhD Theses, IGU, Irkutsk (2001).Google Scholar
- 3.V. I. Zorkaltsev, “Solutions of systems of linear inequalities by interior point algorithms,” in: Modern Optimization Methods and their Applications to Power Engineering Models [in Russian], Nauka, Novosibirsk (2003), pp. 110–141.Google Scholar
- 4.I. I. Dikin and V. I. Zorkaltsev, Iterated Solution of Mathematical Programming Problems (Interior Point Algorithms) [in Russian], Nauka, Novosibirsk (1980).Google Scholar
- 5.V. I. Zorkaltsev and M. A. Kiselyova, Systems of Linear Inequalities [in Russian], IGU, Irkutsk (2007).Google Scholar
- 7.O. N. Voitov, V. I. Zorkaltsev, and A. Yu. Filatov, “Determining feasible modes of electric power engineering systems by interior point algorithms,” Sib. Zhurn. Idustr. Matem., 3, No. 1, 57–65 (2000).Google Scholar
- 8.V. I. Zorkaltsev and D. S. Medvezhonkov, “Numerical experiments with variants of interior point algorithms on nonlinear load flow problems,” in: Control of Large Systems [in Russian], IPU RAN, Moscow, 46, 68–87 (2013).Google Scholar