Abstract:
A method for solving the convex programming problem, which is
ideologically close to the known methods of external penalties, was
proposed. The method uses auxiliary functions that are built on the
general form of the penalty functions. In order to find
approximations, the epigraphs of these auxiliary functions, as well
as the original problem's domain of constraints, were immersed in
certain polyhedral sets. In this regard, the problems of finding the
iterative points are the linear programming problems, in which the
constraints are the sets that approximate the epigraphs and a
polyhedron containing an admissible set. The approximating sets were
constructed using the traditional cutting of iterative points by
planes. The peculiarity of the method is that it enables a
periodic update of the approximating sets by discarding the cutting
planes. The convergence of the proposed method was proved. Its
implementation was discussed.
Citation:
I. Ya. Zabotin, K. E. Kazaeva, “A version of the penalty method with approximation of the epigraphs of auxiliary functions”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 161, no. 2, Kazan University, Kazan, 2019, 263–273
\Bibitem{ZabKaz19}
\by I.~Ya.~Zabotin, K.~E.~Kazaeva
\paper A version of the penalty method with approximation of the epigraphs of auxiliary functions
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2019
\vol 161
\issue 2
\pages 263--273
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1516}
\crossref{https://doi.org/10.26907/2541-7746.2019.2.263-273}
\elib{https://elibrary.ru/item.asp?id=41296516}
Linking options:
https://www.mathnet.ru/eng/uzku1516
https://www.mathnet.ru/eng/uzku/v161/i2/p263
This publication is cited in the following 2 articles:
Igor Zabotin, Oksana Shulgina, Rashid Yarullin, Lecture Notes in Computational Science and Engineering, 141, Mesh Methods for Boundary-Value Problems and Applications, 2022, 575
Rashid Yarullin, Igor Zabotin, Communications in Computer and Information Science, 1661, Mathematical Optimization Theory and Operations Research: Recent Trends, 2022, 204