Abstract:
A family of interior point algorithms for solving linear programs is examined. Under the assumption on the nondegeneracy of the problem, a theoretical justification of these algorithms is given. The sets of the algorithms converging to relatively interior optimal solutions and having linear or superlinear convergence rate are identified.
Key words:
linear programming, interior point method, linear and superlinear convergence of interior point algorithms.
Citation:
V. I. Zorkal'tsev, “On a class of interior point algorithms”, Zh. Vychisl. Mat. Mat. Fiz., 49:12 (2009), 2114–2130; Comput. Math. Math. Phys., 49:12 (2009), 2017–2033
This publication is cited in the following 12 articles:
V. I. Zorkal'tsev, “Interior point method: history and prospects”, Comput. Math. Math. Phys., 59:10 (2019), 1597–1612
V. I. Zorkaltsev, I. V. Mokryi, “Interior point algorithms in linear optimization”, J. Appl. Industr. Math., 12:1 (2018), 191–199
V. I. Zorkal'tsev, “Octahedral projections of a point onto a polyhedron”, Comput. Math. Math. Phys., 58:5 (2018), 813–821
Valery Zorkal'tsev, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017, 1
V. I. Zorkaltsev, “The search for admissible solutions by the interior point algorithms”, Num. Anal. Appl., 9:3 (2016), 191–206
V. I. Zorkaltsev, D. S. Medvezhonkov, “Chislennye eksperimenty s variantami algoritmov vnutrennikh tochek na nelineinykh zadachakh potokoraspredeleniya”, UBS, 46 (2013), 68–87
Zorkaltsev V.I., Perzhabinskii S.M., “Algoritmy vnutrennikh tochek v lineinom i nelineinom programmirovanii”, Omskii nauchnyi vestnik, 2013, no. 1(117), 25–28
V. I. Zorkaltsev, S. M. Perzhabinskii, “Modeli otsenki defitsita moschnosti elektroenergeticheskoi sistemy”, Sib. zhurn. industr. matem., 15:1 (2012), 34–43
Sergey Perzhabinsky, Valery Zorkaltsev, “Model for Power Shortage Estimation in Electric Power Systems”, International Journal of Energy Optimization and Engineering, 1:4 (2012), 70
V. I. Zorkaltsev, “Dual interior point algorithms”, Russian Math. (Iz. VUZ), 55:4 (2011), 26–43
V. G. Zhadan, A. A. Orlov, “O skhodimosti dvoistvennogo metoda Nyutona dlya lineinoi zadachi poluopredelennogo programmirovaniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:2 (2011), 75–90
Citation in format AMSBIB
Contact us: