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 Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 2, Pages 255–263 (Mi zvmmf181)

The method of feasible directions for mathematical programming problems with preconvex constraints

V. I. Zabotin, T. F. Minnibaev

Kazan State Technological University, ul. Karla Marksa 10, Kazan, 420015, Tatarstan, Russia

Abstract: The convergence of the method of feasible directions is proved for the case of the smooth objective function and a constraint in the form of the difference of convex sets (the so-called preconvex set). It is shown that the method converges to the set of stationary points, which generally is narrower than the corresponding set in the case of a smooth function and smooth constraints. The scheme of the proof is similar to that proposed earlier by Karmanov.

Key words: mathematical programming problems with preconvex constraints, classical method of feasible directions, method convergence.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:2, 242–250

Bibliographic databases:

UDC: 519.853

Citation: V. I. Zabotin, T. F. Minnibaev, “The method of feasible directions for mathematical programming problems with preconvex constraints”, Zh. Vychisl. Mat. Mat. Fiz., 48:2 (2008), 255–263; Comput. Math. Math. Phys., 48:2 (2008), 242–250

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. A. Chernyaev, “Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set”, Comput. Math. Math. Phys., 56:10 (2016), 1716–1731
2. V. I. Zabotin, Yu. A. Chernyaev, “Newton's method for minimizing a convex twice differentiable function on a preconvex set”, Comput. Math. Math. Phys., 58:3 (2018), 322–327
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