Geodesic
Minimization of a smooth function on the boundary of an outer generalized spherical segment
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 22-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of minimizing a smooth function on the boundary of the so-called external generalized segment of a sphere, which is constructed in a certain way from a sphere and a convex solid cone with a vertex lying outside the corresponding closed ball. A modification of the gradient projection method is proposed and its convergence to the stationary point of the problem is substantiated.
Keywords: nonconvex optimization, descent method, spherical segment
Mots-clés : gradient projection algorithms. 
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A. M. Dulliev. Minimization of a smooth function on the boundary of an outer generalized spherical segment. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 22-33. http://geodesic.mathdoc.fr/item/VTGU_2024_87_a2/

[1] Dulliev A.M., “Relaksatsionnyi metod minimizatsii gladkoi funktsii na obobschennom segmente sfery”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 54:2 (2014), 208–223 | DOI | MR | Zbl

[2] Zabotin V.I., Chernyaev Yu.A., “Obobschenie metoda proektsii gradienta na ekstremalnye zadachi s predvypuklymi ogranicheniyami”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 41:3 (2001), 367–373 | MR | Zbl

[3] Chernyaev Yu.A., “Iteratsionnyi algoritm minimizatsii vypukloi funktsii na pereseche nii sfericheskoi poverkhnosti i vypuklogo kompaktnogo mnozhestva”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 57:10 (2017), 1631–1640 | DOI | Zbl

[4] Chernyaev Yu.A., “Metod proektsii gradienta dlya ekstremalnykh zadach s ogranicheniem v vide peresecheniya gladkoi poverkhnosti i vypuklogo zamknutogo mnozhestva”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 59:1 (2019), 37–49 | DOI | Zbl

[5] Nesterov Yu.E., Vvedenie v vypukluyu optimizatsiyu, Izd-vo MTsNMO, M., 2010, 279 pp.