Abstract:
We consider the convex programming problem in a reflexive space with operator equality constraint and finite number of functional inequality constraints. For this problem we prove the stable with respect to the errors in the initial data Lagrange principle in sequential nondifferential form. It is shown that the sequential approach and dual regularization significantly expand a class of optimization problems that can be solved on a base of the classical design of the Lagrange function. We discuss the possibility of its applicability for solving unstable optimization problems.
Citation:
A. A. Gorshkov, M. I. Sumin, “Stable Lagrange principle in sequential form for the problem of convex programming in uniformly convex space and its applications”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 1, 14–28; Russian Math. (Iz. VUZ), 59:1 (2015), 11–23
\Bibitem{GorSum15}
\by A.~A.~Gorshkov, M.~I.~Sumin
\paper Stable Lagrange principle in sequential form for the problem of convex programming in uniformly convex space and its applications
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 1
\pages 14--28
\mathnet{http://mi.mathnet.ru/ivm8962}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 1
\pages 11--23
\crossref{https://doi.org/10.3103/S1066369X15010028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920854793}
Linking options:
https://www.mathnet.ru/eng/ivm8962
https://www.mathnet.ru/eng/ivm/y2015/i1/p14
This publication is cited in the following 1 articles:
A. A. Gorshkov, M. I. Sumin, “Regulyarizatsiya printsipa maksimuma Pontryagina v zadache optimalnogo granichnogo upravleniya dlya parabolicheskogo uravneniya s fazovymi ogranicheniyami v lebegovykh prostranstvakh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 162–177
Citation in format AMSBIB
Contact us: