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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 1983, Volume 23, Number 1, Pages 61–72 (Mi zvmmf5629)  
A parametric method of linearization in mathematical programming problems

V. M. Panin, B. N. Pshenichnyi

Kiev
Full-text PDF (1345 kB)
Abstract: The mathematical programming problem with constraints in the form of convex inequalities, and a method of linearization for solving the problem, are studied. It is shown that the method has all the properties of the classical gradient descent method, widely used in unconstrained optimization problems. The method does not employ evaluations of the second derivatives or their approximation, and converges with an arbitrarily chosen initial approximation.
Received: 30.03.1981
Revised: 03.06.1982
English version:
USSR Computational Mathematics and Mathematical Physics, 1983, Volume 23, Issue 1, Pages 42–49
DOI: https://doi.org/10.1016/S0041-5553(83)80008-1
Bibliographic databases:
Document Type: Article
UDC: 519.85
Language: Russian
Citation: V. M. Panin, B. N. Pshenichnyi, “A parametric method of linearization in mathematical programming problems”, Zh. Vychisl. Mat. Mat. Fiz., 23:1 (1983), 61–72; U.S.S.R. Comput. Math. Math. Phys., 23:1 (1983), 42–49
Citation in format AMSBIB
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\by V.~M.~Panin, B.~N.~Pshenichnyi
\paper A parametric method of linearization in mathematical programming problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1983
\vol 23
\issue 1
\pages 61--72
\mathnet{http://mi.mathnet.ru/zvmmf5629}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=692741}
\zmath{https://zbmath.org/?q=an:0537.90085|0518.90067}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1983
\vol 23
\issue 1
\pages 42--49
\crossref{https://doi.org/10.1016/S0041-5553(83)80008-1}
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