Geodesic
Sets convex in a~cone of directions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 73-76.

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We consider sets which are convex in directions from some cone $K$. We generalize some well-known properties of ordinary convex sets for the case of $K$-convex sets and give some applications in optimization theory.
Keywords: $K$-convex sets, separability, cones, convex hull. 
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M. A. Sevodin. Sets convex in a~cone of directions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 73-76. http://geodesic.mathdoc.fr/item/IVM_2013_10_a7/

[1] Zangvill U. I., Nelineinoe programmirovanie. Edinyi podkhod, Sov. radio, M., 1973

[2] Soltan V. P., Vvedenie v aksiomaticheskuyu teoriyu vypuklosti, Shtiintsa, Kishinev, 1984 | MR | Zbl

[3] Andramonov M. Yu., Metody globalnoi minimizatsii dlya nekotorykh klassov obobschenno vypuklykh funktsii, Izd-vo Kazansk. matem. o-va, Kazan, 2001

[4] Robertson M. S., “Analytic functions starlike in one direction”, Amer. J. Math., 58 (1936), 465–472 | DOI | MR | Zbl

[5] Aksentev L. A., Shabalin P. L., “Usloviya odnolistnosti s kvazikonformnym prodolzheniem i ikh primenenie”, Izv. vuzov. Matem., 1983, no. 2, 6–14 | MR | Zbl

[6] Sevodin M. A., “Ravnovesnye i pareto-optimalnye raspredeleniya v ekonomike obmena s nevypuklymi predpochteniyami potrebitelei”, Ekonomika, statistika i informatika. Vestn. UMO, 2011, no. 3, 149–154

[7] Sevodin M. A., Gavrilova M. O., “O svoistve vneshnei neekonomichnosti v zadache vyravnivaniya tsen na faktory proizvodstva”, Vestn. OGU, 2007, no. 10, 69–73

[8] Gavrilova M. O., Sevodin M. A., “O suschestvovanii ravnovesiya v ekonomike obmena s odnim klassom nevypuklykh predpochtenii potrebitelei”, Uchen. zap. Kazansk. un-ta. Ser. fiz.-matem. nauki, 153, no. 1, 2011, 240–248 | Zbl