Abstract
On the basis of the approach proposed, we obtain new estimates of extremal values of strongly convex differentiable functions and strengthened estimates of minima on a set of combinations with repetions.
References
Yu. G. Stoyan and O. A. Emets,Theory and Methods of Euclidean Combinatorial Optimization [in Russian], Institute of System Investigations in Education, Kiev (1993).
Yu. G. Stoyan,Some Properties of Special Combinatorial Sets [in Russian], Preprint No. 85, Institute of Problems of Machine Building of the Academy of Sciences of Ukraine, Kharkov (1980).
O. A. Emets,Theory and Methods of Combinatorial Optimization on Euclidean Sets in Geometric Projection [in Ukrainian], Author’s Abstract of the Doctoral-Degree Thesis, Kiev (1997).
O. A. Emest, “On optimization of convex functions on a Euclidean combinatorial set of polypermutations,”Zh. Vychisl. Mat. Mat. Fiz., No. 6, 855–869 (1994).
O. A. Emets, “On extremal properties of nondifferentiable convex functions on a Euclidean set of combinations with repetitions”Ukr. Mat. Zh.,46, No. 6. 680–691 (1994).
Additional information
Poltava Technical University, Poltava. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 118–1121, August, 1999.
Rights and permissions
About this article
Cite this article
Emets, O.A., Roskladka, A.A. On estimates of minima of criterion functions in optimization on combinations. Ukr Math J 51, 1262–1265 (1999). https://doi.org/10.1007/BF02592514
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02592514