Theoretical justification of interior point algorithms for solving optimization problems with nonlinear constraints
Tóm tắt
A family of interior point algorithms is considered. These algorithms can be used for solving mathematical programming problems with nonlinear inequality constraints. Some weighted Euclidean norms are applied to finding a descent direction for improving the solution. These norms vary with iterations. A theoretical justification of the algorithms with some assumptions (including the nonsingularity of the problem) is presented.
Tài liệu tham khảo
Dikin, I.I., Iterative Solution of Linear andQuadratic Programming Problems, Dokl. Ross. Akad.Nauk, 1967, vol. 174, pp. 747–748.
Dikin, I.I. and Zorkaltsev, V.I., Iterativnoe reshenie zadach matematicheskogo programmirovaniya (Iterative Solution of Mathematical Programming Problems (Algorithms of the Interior Point Method)), Novosibirsk: Nauka, 1980.
Evtushenko, Yu.G. and Zhadan, V.G., Numerical Methods of Solving Some Operations Research Problems, Zh. Vych. Mat. Mat. Fiz., 1973, vol. 13, no. 3, pp. 583–597.
Evtushenko, Yu.G. and Zhadan, V.G., Barrier-Projective Methods of Solving Nonlinear Programming Problems, Zh. Vych. Mat. Mat. Fiz., 1994, vol. 34, no. 5, pp. 669–684.
Zorkaltsev, V.I., Otnositel’no vnutrennyaya tochka optimal’nykh reshrnii (A Relatively Interior Point of Optimal Solutions), Syktyvkar: Komi Branch of the USSR Acad. Sci., 1984.
Zorkaltsev, V.I., Metod otnositel’no vnutrennyikh tochek (Method of Relatively Interior Points), Syktyvkar: Komi Branch of the USSR Acad. Sci., 1986.
Zangwill, W.I., Nelineinoe programmirovanie (Nonlinear Programming), Moscow: Sovetskoe Radio, 1973.
Perzhabinsky, S.M., Interior Point Algorithm with Quadratic Approximations, in Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie (Modern Technologies. System Analysis. Modeling), Irkutsk: Irkutsk State University of Means of Communication, 2008, vol. 18, no. 3, pp. 97–101.