Geodesic
On estimates for solutions of systems of convex inequalities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1486-1492 Cet article a éte moissonné depuis la source Math-Net.Ru

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The distance from a given point to the solution set of a system of strict and nonstrict inequalities described by convex functions is estimated. As consequences, estimates for the distance from a given point to the Lebesgue set of a convex function are obtained and sufficient conditions for convex-valued set-valued mappings to be covering are established. 
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A. V. Arutyunov; S. E. Zhukovskiy. On estimates for solutions of systems of convex inequalities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1486-1492. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a3/

[1] Vasilev F. P., Ivanitskii A. Yu., Lineinoe programmirovanie, Faktorial, M., 1998 | MR

[2] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979 | MR

[3] Izmailov A. F., Solodov M. F., Chislennye metody optimizatsii, Fizmatlit, M., 2005

[4] Pang J.-Sh., “Error bounds in mathematical programming”, Math. Programming, 79 (1997), 299–332 | MR | Zbl

[5] Facchinei F., Pang J.-Sh., Finite-dimentional variational inequalities and complementary problems, Springer, New York, 2003

[6] Ter-Krikorov A. M., “Vypukloe programmirovanie v prostranstve, sopryazhennom prostranstvu Banakha, i vypuklye zadachi optimalnogo upravleniya s fazovymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 16:2 (1976), 351–358 | MR | Zbl

[7] Arutyunov A. V., “Nakryvayuschie otobrazheniya v metricheskikh prostranstvakh i nepodvizhnye tochki”, Dokl. AN, 416:2 (2007), 151–155 | MR | Zbl

[8] Arutyunov A. V., “Iteratsionnyi metod nakhozhdeniya tochek sovpadeniya dvukh otobrazhenii”, Zh. vychisl. matem. i matem. fiz., 52:1 (2012), 1947–1950 | Zbl

[9] Lewis A. S., Pang J.-S., “Error bounds for convex inequality systems”, Proc. fifth Internat. Symposium of Generalized Convexity (Luminy, 1996)

[10] Mangasarian O. L., Error bounds for nondifferentiable convex inequalities under a strong slater constrait qualification, Math. Programming Technical Report 96-04, Computer Science Department, University of Wisconsin-Madison, July 1996 | MR

[11] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[12] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR

[13] Zalmai G. J., “A continuous-time generalization of Gordan's transposition theorem”, J. Math. Anal. Appl., 110 (1985), 130–140 | DOI | MR | Zbl