Geodesic
Algorithms for projecting a point onto a level surface of a continuous function on a compact set
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 9, pp. 1448-1454 
N. K. Arutyunova; A. M. Dulliev; V. I. Zabotin. Algorithms for projecting a point onto a level surface of a continuous function on a compact set. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 9, pp. 1448-1454. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_9_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Given an equation $f(x)=0$, the problem of finding its solution nearest to a given point is considered. In contrast to the authors’ previous works dealing with this problem, exact algorithms are proposed assuming that the function $f$ is continuous on a compact set. The convergence of the algorithms is proved, and their performance is illustrated with test examples.

[1] Bauschke H. H., Borwein J. M., “On projection algorithms for solving convex feasibility problems”, SIAM Review, 38:3 (1996), 367–426 | DOI

[2] Pang C. H. J., Set intersection problems: Supporting hyperplanes and quadratic programming, 2012, arXiv: 1212.6843v1

[3] Nurminskii E. A., “O skhodimosti metoda podkhodyaschikh affinnykh podprostranstv dlya resheniya zadachi o naimenshem rasstoyanii do simpleksa”, Zh. vychisl. matem. i matem. fiz., 45:11 (2005), 1991–1999

[4] Tuy H., Al-Khayyal F., Thach P. T., “Monotonic optimization: Branch and cut methods”, Essays and Surveys in Global Optimization, eds. C. Audet, P. Hansen, G. Savard, Springer, 2005, 39–78 | DOI

[5] Ortega Dzh., Reinbolt V., Iteratsionnye metody resheniya nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1975

[6] Zabotin V. I., Dulliev A. M., “Iteratsionnyi algoritm proektirovaniya tochki na nevypukloe mnogoobrazie v lineinom normirovannom prostranstve”, Zh. vychisl. matem. i matem. fiz., 44:5 (2004), 827–830

[7] Zabotin V. I., Arutyunova N. K., “Dva algoritma otyskaniya proektsii tochki na nevypukloe mnozhestvo v normirovannom prostranstve”, Zh. vychisl. matem. i matem. fiz., 53:3 (2013), 344–349 | DOI

[8] Vanderbei R. J., “Extension of Piyavskii's algorithm to continuous global optimization”, J. Global Optimization, 14 (1999), 205–216 | DOI