Geodesic
Minimization of a~quadratic function on the sphere
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 329-338.

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In this paper, a sequential algorithm for solving the problem of minimization of a quadratic function on a sphere is proposed. At each iteration of the scheme, a two-dimensional problem of minimization is solved. Numerical comparisons with other methods are presented. 
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E. A. Kotel'nikov. Minimization of a~quadratic function on the sphere. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 329-338. http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a1/

[1] Hager W. W., “Minimizing a quadratic over a sphere”, SIAM J. Optim., 12:1 (2001), 188–208 | DOI | MR | Zbl

[2] Dennis Dzh., Shnabel R., Chislennye metody bezuslovnoi optimizatsii i resheniya nelineinykh uravnenii, Mir, M., 1988 | MR | Zbl

[3] Zabinyako G. I., Khodaev Yu. V., “O primenenii metoda doveritelnoi oblasti k minimizatsii funktsii”, Tr. Vychislitelnogo tsentra SO RAN. Ser. Sistemnoe modelirovanie, 3(21), Novosibirsk, 1995, 47–54

[4] Kotelnikov E. A., “Ob odnom sposobe vybora shaga v metode doveritelnoi oblasti”, Problemy informatiki, 1:18 (2013), 16–26