Basaeva, Elena K.; Kusraev, Anatoly G.; Kutateladze, Semen S. Quaisidifferentials in Kantorovich spaces. (English) Zbl 1353.49016 J. Optim. Theory Appl. 171, No. 2, 365-383 (2016). Summary: This is an overview of the quasidifferential calculus for the mappings that arrive at Kantorovich spaces. Necessary optimality conditions are derived also for multiple criteria optimization problems with quasidifferentiable data. Cited in 4 Documents MSC: 49J52 Nonsmooth analysis 49K27 Optimality conditions for problems in abstract spaces 49J27 Existence theories for problems in abstract spaces Keywords:Kantorovich space; sublinear operator; quasidifferentials; nonsmooth extremal problem PDF BibTeX XML Cite \textit{E. K. Basaeva} et al., J. Optim. Theory Appl. 171, No. 2, 365--383 (2016; Zbl 1353.49016) Full Text: DOI arXiv OpenURL References: [1] Demyanov, VF; Rubinov, AM, On quasidifferentiable functionals, Sov. Math. Dokl., 250, 21-25, (1980) · Zbl 0456.49016 [2] Demyanov, V.F., Dixon, L.C.W.: Quasidifferential Calculus. North-Holland, Amsterdam (1986) · Zbl 0583.00012 [3] Demyanov, V.F., Rubinov, A.M.: Quasidifferential Calculus. Optimization Software, New York (1986) · Zbl 0712.49012 [4] Demyanov, V.F., Rubinov, A.M.: Fundamentals of Nonsmooth Analysis and Quasidifferential Calculus. Nauka, Moscow (1990) [5] Demyanov, V.F., Stavroulaskis, G.E., Polyakova, L.N., Panagiotopoulos, P.D.: Quasidifferentiability and Nonsmooth Modelling in Mechanics. Engineering and Economics. Kluwer, Dordrecht (1996) [6] Demyanov, V.F., Rubinov, A.M.: Quasidifferentiability and Related Topics. Kluwer, Dordrecht (2000) · Zbl 0949.00047 [7] Kusraev, A.G., Kutateladze, S.S.: Subdifferential Calculus: Theory and Applications. Nauka, Moscow (2007) · Zbl 1137.49002 [8] Vulikh, B.Z.: Introduction to the Theory of Semi-Ordered Spaces. Fizmatgiz, Moscow (1961) · Zbl 0101.08501 [9] Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Nauka, Moscow (1984) · Zbl 0555.46001 [10] Kantorovich, L.V., Vulikh, B.Z., Pinsker, A.G.: Functional Analysis in Semi-Ordered Spaces. Gostekhizdat, Moscow and Leningrad (1950) · Zbl 0037.07201 [11] Kusraev, A.G.: Dominated Operators. Kluwer, Dordrecht (2000) · Zbl 0983.47025 [12] Kantorovich, LV, To the general theory of operations in semi-ordered spaces, Sov. Math. Dokl., 1, 271-274, (1936) [13] Levin, V.L.: Convex Analysis in Measurable Function Spaces and Its Applications in Mathematics and Economics. Nauka, Moscow (1985) [14] Kusraev, A.G., Kutateladze, S.S.: Boolean Valued Analysis. Kluwer, Dordrecht (1999) · Zbl 0955.46046 [15] Kusraev, A.G., Kutateladze, S.S.: Boolean Valued Analysis: Selected Topics. Southern Mathematical Institute, Vladikavkaz (2014) · Zbl 1407.46003 [16] Riesz, F.: Sur la décomposition des opérations fonctionnelles. In: Atti Congresso Intern. Bologna, 1928, vol. 3, pp. 143-148 (1930) [17] Demyanov, VF; Rubinov, AM, On quasidifferentiable mappings, Math. Operationsforsch. Stat. Ser. Optim., 14, 3-21, (1983) · Zbl 0517.90065 [18] Demyanov, V.F., Polyakova, L.N., Rubinov, A.M.: On one generalization of the concept of subdifferential. In: Abstracts. All-Union Conference on Dynamical Control. Sverdlovsk, pp. 79-84 (1979) [19] Basaeva, EK, Quasidifferentials in \(K\)-spaces, Vladikavkaz Math. J., 5, 14-30, (2003) · Zbl 1051.46027 [20] Basaeva, EK; Kusraev, AG, On the quasidifferential of composition, Vladikavkaz Math. J., 5, 10-25, (2003) · Zbl 1051.46028 [21] Demyanov, V.F., Vasiliev, L.V.: Nondifferentiable Optimization. Nauka, Moscow (1981) [22] Gorokhovik, VV, On the quasidifferentiability of real-valued functions, Sov. Math. Dokl., 266, 1294-1298, (1982) · Zbl 0598.26013 [23] Gorokhovik, VV, On the quasidifferentiability of real functions and the conditions of local extrema, Sib. Math. J., 25, 62-70, (1984) [24] Basaeva, EK, Necessary optimality conditions in quasidifferentiable vector programs, Vladikavkaz Math. J., 6, 3-25, (2004) · Zbl 1113.90362 [25] Kusraev, A.G.: Vector Duality and its Applications. Nauka, Novosibirsk (1985) · Zbl 0616.49010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.