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З. О классе почти–дифференцируемых функций и одном метод минимизациифункций этого класс // Кибернетика. 1972. № 4. С. 65–70.[58] Шор Н.З. Методы минимизации недифференцируемых функций и их приложения.Киев: Наукова думка, 1979. 200 с.134[59] Эдвардс Р. Функциональный анализ. М.: Мир, 1969.
1071 с.[60] Экланд И., Темам Р. Выпуклый анализ и вариационные проблемы. М.: Мир, 1979.400 с.[61] Энгелькинг Р. Общая топология. М.: Мир, 1986. 752 с.[62] Abbasov M.E., Demyanov V.F. Proper and adjoint exhauster in nonsmooth analysis:optimality conditions // J. Glob. Optim. 2013. Vol. 56, no. 2. pp.
569–585.[63] Adams R.A. Sobolev Spaces. New York: Academic Press, 1975. 268 p.[64] Aubin J.–P., Frankowska H. Set–valued analysis. Boston: Birkhauser, 1990. 461 p.[65] Aubin J.–P., Cellina A. Differential Inclusions. Berlin: Springer–Verlag, 1984. 364 p.[66] Banach S. Über die Baire’sche Kategorie gewisser Funktionenmengen // Studia Math.1931. Vol. 3. pp. 174–179.[67] Borwein J.M., Zhu Q.J. A survey of subdifferential calculus with applications //Nonlinear Analysis: Theory, Methods and Applications. 1999. Vol. 38, no. 6. pp.
687–773.[68] Avis D., Bremner D., Seidel R. How good are convex hull algorithms? // Comput.Geom. Theory and Appl. 1997. Vol. 7, Nos. 5–6. pp. 265–302.[69] Bagirov A. M., Nazari Ganjehlou A., Ugon J., Tor A.H. Truncated codifferentialmethod for nonsmooth convex optimization // Pac. J. Optim. 2010.
Vol. 6, no. 3. pp. 483–496.[70] Bagirov A.M., Ugon J. Codifferential method for minimizing DC functions // J. Glob.Optim. 2011. Vol. 50, no. 1. pp. 3–22.[71] Barber C.B., Dobkin D.P., Huhdanpaa H. The quickhull algorithm for convex hulls// ACM Trans. on Mathematical Software. 1996. Vol. 22, no. 4. pp. 469–483.[72] Bartels S.G., Pallaschke D.
Some remarks on the space of differences of sublinearfunctions // Applicationes Matematicae. 1993. Vol. 22, no. 3. pp. 419–426.[73] Bet–Tal A., Ben–Israel A. F –convex functions: properties and applications / GeneralizedConcavity in Optimization and Economics; S. Schaible and W.T. Ziemba eds. New York:Academic Press, 1981.
pp. 301–334.135[74] Clarke F.H. The Euler–Lagrange differential inclusion // J. Differential Eq. 1975. Vol. 19,no. 1. pp. 80–90.[75] Clarke F.H., Ledyaev Y.S., Stern R.J., Wolenski P.R. Nonsmooth analysis andControl Theory. New York: Springer–Verlag, 1998. 278 p.[76] Dacorogna B. Direct Methods in the Calculus of Variations, New York: SpringerScience+Business Media, LLC, 2008. 634 p.[77] Demyanov V.F. On codifferentiable functions // Vestn. Leningr.
Univ., Math. 1988. Vol.21. pp. 27–33.[78] Demyanov V.F. Continuous generalized gradients for nonsmooth functions / Lecture Notesin Economics and Mathematical Systems, vol. 304; A. Kurzhanski, K. Neumann and D.Pallaschke, eds. Berlin: Springer, 1988, pp. 24–27.[79] Demyanov V.F. Exhauster of a positively homogeneous function // Optimization. 1999.Vol. 45, Nos. 1–4. pp. 13 – 29.[80] Demyanov V.F. Exhausters and convexificators — new tools in nonsmooth analysis /Quasidifferentiability and Related Topics; V.F.
Demyanov and A.M. Rubinov eds. Dordrecht:Kluwer Acad. Publ., 2000. pp. 85–137.[81] Demyanov V.F. Conditions for an Extremum in Metric Spaces // J. Glob. Optim. 2000.Vol. 17, Nos. 1–4. pp. 55–63.[82] Demyanov V.F., Bagirov A.M., Rubinov A.M.
A method of truncated codifferentialwith application to some problems of cluster analysis // J. Glob. Optim. 2002. Vol. 23, no.1. pp. 63–80.[83] Demyanov V.F., Roshchina V.A. Constrained optimality conditions in terms of properand adjoint exhausters // Appl. Comput. Math. 2005. Vol.
4, no. 2. pp. 114–124.[84] Demyanov V.F. Roschina V.A. Optimality conditions in terms of upper and lowerexhausters // Optimization. 2006. Vol. 55, Nos. 5–6. pp. 525–540.[85] DemyanovV.F.,RubinovA.M. On quasidifferentiable mappings // Math.Operationsforsch. Statist. Ser. Optim. 1983. Vol. 14. pp. 3–21.[86] Demyanov V. F., Tamasyan G. Sh. Exact penalty functions in isoperimetric problems// Optimization. 2010. Vol. 60.
no. 8. pp. 1-25.136[87] Demyanov V.F., Stavroulakis G., Polyakova L.N., Panagiotopoulos P.D.Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics.Dordrecht, London: Kluwer Academic Publishers, 1996. 348 p.[88] Dolgopolik M.V. Nonsmooth problems of Calculus of Variations with a codifferentiableintegrand / Конструктивный негладкий анализ и смежные вопросы. Тезисы докладов международной конференции. СПб.: Изд–во Санкт–Петербургского университета,2012. С.46–48.[89] Dolgopolik M.V. Abstract Convex Approximations of Nonsmooth Functions //Optimization. 2014. DOI: 10.1080/02331934.2013.869811.[90] Dolgopolik M.V., Tamasyan G.Sh. Method of Steepest Descent for Two–DimensionalProblems of Calculus of Variations / Constructive Nonsmooth Analysis and Related Topics,Springer Optimization and Its Applications, vol.
87; Demyanov V., Pardalos P.M. andBatsyn M., eds. Springer. New York: Springer Science+Business Media, 2014. pp. 101–113.[91] Giannessi F. Semidifferentiable functions and necessary optimality conditions // J. Optim.Theory Appl. 1989. Vol. 60, no. 2. pp. 191–241.[92] Giannesssi F. Constrained Optimization and Image Space Analysis: Volume 1: Separationof Sets and Optimality Conditions. New York: Springer Science+Business Media, 2005.395 p.[93] Halkin H. Necessary conditions in mathematical programming and optimal control theory// Lect.
Notes Econ. Math. Syst. 1974. Vol. 105. pp. 113–165.[94] Hiriart–Urruty J.–B., Lemaréchal C. Convex Analysis and Minimization Algorithms.Volume I. Berline, Heidelberg: Springer–Verlag, 1993. 417 p.[95] Hiriart–Urruty J.–B., Lemaréchal C. Convex Analysis and Minimization Algorithms.Volume II. Berlin, Heidelberg: Springer–Verlag, 1993. 347 p.[96] Hu S., Papageorgiou N.S.
Handbook of Multivalued Analysis: Volume I: Theory.Dordrecht: Kluwer Academic Publishers, 1997. 980 p.[97] Hu S., Papageorgiou N.S. Handbook of Multivalued Analysis: Volume II: Applications.Dordrecht: Kluwer Academic Publishers, 2000. 944 p.137[98] Hunt B. R. The prevalence of continuous nowhere differentiable functions // Proceedingsof the American Mathematical Society. 1994. Vol.
122, no. 3. pp. 711–717.[99] Ioffe A.D. Nonsmooth Analysis: differential calculus of nondifferentiable functions // Tran.Amer. Math. Soc. 1981. Vol. 266, no. 1. pp. 1–55.[100] Ioffe A. D. Metric regularity and subdifferential calculus // Russian Math. Surveys. 2000.Vol. 55, no. 3. pp. 501-558.[101] Ioffe A. D.
Abstract convexity and non–smooth analysis // Adv. Math. Econ. 2001. Vol.3. pp. 45–61.[102] Ioffe A.D., Rockafellar R.T. The Euler and Weierstrass conditions for nonsmoothvariational problems // Calculus of Variations and Partial Differential Equations. 1996.Vol. 4, no.
1. pp. 59–87.[103] Ishizuka Yo. Optimality conditions for quasidifferentiable programs with application totwo–level optimization // SIAM J. Control and Optimization. 1988. Vol. 26, no. 6. pp. 1388–1398.[104] Kruger A. Ya. On Fréchet subdifferentials // Journal of Mathematical Sciences. 2003. Vol.116, no. 3. pp. 3325–3358.[105] Kuntz L. A characterization of continuously codifferentiable functions and someconsequences // Optimization. 1991. Vol.
22, no. 4. pp. 539–547.[106] Levi F.W. On Helly’s theorem and the axioms of convexity // J. Indian Math. Soc. ParA. 1951. Vol. 15, pp. 65–76.[107] Luderer B., Rosiger R., Wurker U. On necessary minimum conditions inquasidifferential calculus: independence on the specific choice of quasidifferential //Optimization. 1991.
Vol. 22, no. 5. pp. 643–660.[108] Mordukhovich B.S. Variational Analysis and Generalized Differentiation I. Basic Theory.Berlin, Heidelber, New York: Springer, 2006. 582 p.[109] Mordukhovich B.S. Variational Analysis and Generalized Differentiation II. Applications.Berlin, Heidelberg, New York: Springer, 2006. 612 p.[110] Nesterov Y. Introductory Lectures on Convex Optimization. A Basic Course. Dordrecht:Kluwer Academic Publishers, 2004.
236 p.138[111] Pallaschke D., Rolewicz S. Foundations of mathematical optimization. Convex analysiswithout linearity. Dordrecht: Kluwer Academic Publishers, 1997. 582 p.[112] Pallaschke D., Urbański R. Pairs of Compact Convex Sets. Factional Arithmetic withConvex Sets. Dordrecht: Kluwer Academic Publishers, 2002. 295 p.[113] Pallaschke D., Recht P., Urbański R. On locally-Lipschitz quasi-differentiable functionsin Banach spaces // Optim. 1986. Vol.
17, no. 3. pp. 287–295.[114] Penot J.–P. Calculus Without Derivatives. New York: Springer Science+Business Media,2013. 544 p.[115] Radström H. An embedding theorem for spaces of convex sets // Proc. Amer. Math. Soc.1952. Vol. 3, no. 1, pp. 165–169.[116] Rockafellar R.T. Conjugate convex functions in optimal control and the calculus ofvariations // J. Math. Anal. Appl. 1970.
Vol. 32, no. 1. pp. 174–222.[117] Rockafellar R.T., Wets R.J.B. Variational Analysis. Berlin: Springer, 1998. 734 p.[118] Rolewicz S. Φ–convex functions defined on metric spaces // J. Math. Sciences. 2003. Vol.115, no. 5. pp. 2631–2651.[119] Rubinov A.M. Abstract Convexity and Global Optimization. Boston, Dordrecht, London:Kluwer Academic Publishers, 2000.
490 p.[120] Rubinov A.M. Abstract convexity: examples and applications // Optimization. 2000. Vol.47, Nos. 1–2. pp. 1–33.[121] Rubinov A.M., Zaffaroni A. Continuous approximation of nonsmooth mappings /Progress in optimization: contributions from Australia; A. Eberhard, R. Hill, D. Ralph andB. Glover, eds. Dordrecht: Kluwer Academic Publishers, 1999. pp. 57–86.[122] Schirotzek W. Nonsmooth analysis. Berling, Heidelberg: Springer, 2007. 373 p.[123] Singer I. Surrogate Conjugate Functions and Surrogate Convexity // Applicable Analysis.1983. Vol.
16, no. 4. pp. 291–327.[124] Singer I. Abstract Convex Analysis. New York: Wiley–Interscience Publication, 1997. 491 p.139[125] Uderzo A. Convex approximators, convexificators and exhausters: applications toconstrained extremum problem / Quasidifferentiability and related Topics; V.F. Demyanovand A.M. Rubinov, eds. Dordrecht: Kluwer Academic Publishers, 2000. pp. 297–327.[126] Uderzo A. Fréchet quasidifferential calculus with applications to metric regularity ofcontinuous maps // Optim. 2005. Vol.
54, Nos. 4–5. pp. 469–493.[127] Zaffaroni A. Continuous approximations, codifferentiable functions and minimizationmethods / Quasidifferentiability and related Topics; V.F. Demyanov and A.M. Rubinov,eds. Dordrecht: Kluwer Academic Publishers, 2000.
pp. 361–391.[128] Zălinescu C Convex analysis in general vector spaces. Singapore: World ScientificPublishing Co. Pte. Ltd., 2002. 367 p.140.
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