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Generalized exhausters: Existence, construction, optimality conditions
1. | Saint Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, Russian Federation |
References:
[1] |
M. E. Abbasov, Extremality conditions in terms of adjoint exhausters, (In Russian) Vestnik of Saint-Petersburg University; Applied mathematics, informatics, control processes. 10 (2011), 3-8. |
[2] |
M. E. Abbasov and V. F. Demyanov, Extremum Conditions for a Nonsmooth Function in Terms of Exhausters and Coexhausters, (In Russian) Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 4. English translation: Proceedings of the Steklov Institute of Mathematics, 2010, Suppl. 2, pp. S1-S10. Pleiades Publishing, Ltd. (2010). |
[3] |
M. E. Abbasov and V. F. Demyanov, Proper and adjoint exhausters in Nonsmooth analysis: Optimality conditions, Journal of Global Optimization, 56 (2013), 569-585.
doi: 10.1007/s10898-012-9873-8. |
[4] |
M. Castellani, A dual representation for proper positively homogeneous functions, J. Global Optim., 16 (2000), 393-400.
doi: 10.1023/A:1008394516838. |
[5] |
V. F. Demyanov, Optimality Conditions and Variational Calculus, (In Russian). Moscow, Higher School Publishing, 2005. |
[6] |
V. F. Demyanov, Exhausters and convexificators - new tools in nonsmooth analysis, Nonconvex Optim. Appl., Kluwer Acad. Publ., Dordrecht, Quasidifferentiability and related topics, 43 (2000), 85-137.
doi: 10.1007/978-1-4757-3137-8_4. |
[7] |
V. F. Demyanov, Proper Exhausters and Coexhausters in Nonsmooth Analysis, Optimization, 61 (2012), 1347-1368.
doi: 10.1080/02331934.2012.700929. |
[8] |
V. F. Demyanov, Exhausters of a positively homogeneous function, Optimization, 45 (1999), 13-29.
doi: 10.1080/02331939908844424. |
[9] |
V. F. Demyanov and V. A. Roschina, Optimality conditions in terms of upper and lower exhausters, Optimization, 55 (2006), 525-540.
doi: 10.1080/02331930600815777. |
[10] |
V. F. Demyanov and A. M. Rubinov, Constructive Nonsmooth Analysis, Approximation & Optimization, 7. Peter Lang, Frankfurt am Main, 1995. iv+416 pp. |
[11] |
V. F. Demyanov and A. M. Rubinov, Exhaustive families of approximations revisited,From convexity to nonconvexity, Nonconvex Optim. Appl., Kluwer Acad. Publ., Dordrecht, 55 (2001), 43-50.
doi: 10.1007/978-1-4613-0287-2_4. |
[12] |
B. N. Pshenichny, Convex Analysis and Extremal Problems (in Russian). Nauka, Moscow, 1980, 320 pp. |
[13] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton University Press, Princeton, N.J. 1970. |
[14] |
V. A. Roshchina, Limited exhausters and optimality conditions, Control Processes and Stability: Proceedings of the 36-th international conference of students and graduate students, Saint-Petresburg, Saint-Petrsburg State University Press, (2005), 521-524. |
show all references
References:
[1] |
M. E. Abbasov, Extremality conditions in terms of adjoint exhausters, (In Russian) Vestnik of Saint-Petersburg University; Applied mathematics, informatics, control processes. 10 (2011), 3-8. |
[2] |
M. E. Abbasov and V. F. Demyanov, Extremum Conditions for a Nonsmooth Function in Terms of Exhausters and Coexhausters, (In Russian) Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 4. English translation: Proceedings of the Steklov Institute of Mathematics, 2010, Suppl. 2, pp. S1-S10. Pleiades Publishing, Ltd. (2010). |
[3] |
M. E. Abbasov and V. F. Demyanov, Proper and adjoint exhausters in Nonsmooth analysis: Optimality conditions, Journal of Global Optimization, 56 (2013), 569-585.
doi: 10.1007/s10898-012-9873-8. |
[4] |
M. Castellani, A dual representation for proper positively homogeneous functions, J. Global Optim., 16 (2000), 393-400.
doi: 10.1023/A:1008394516838. |
[5] |
V. F. Demyanov, Optimality Conditions and Variational Calculus, (In Russian). Moscow, Higher School Publishing, 2005. |
[6] |
V. F. Demyanov, Exhausters and convexificators - new tools in nonsmooth analysis, Nonconvex Optim. Appl., Kluwer Acad. Publ., Dordrecht, Quasidifferentiability and related topics, 43 (2000), 85-137.
doi: 10.1007/978-1-4757-3137-8_4. |
[7] |
V. F. Demyanov, Proper Exhausters and Coexhausters in Nonsmooth Analysis, Optimization, 61 (2012), 1347-1368.
doi: 10.1080/02331934.2012.700929. |
[8] |
V. F. Demyanov, Exhausters of a positively homogeneous function, Optimization, 45 (1999), 13-29.
doi: 10.1080/02331939908844424. |
[9] |
V. F. Demyanov and V. A. Roschina, Optimality conditions in terms of upper and lower exhausters, Optimization, 55 (2006), 525-540.
doi: 10.1080/02331930600815777. |
[10] |
V. F. Demyanov and A. M. Rubinov, Constructive Nonsmooth Analysis, Approximation & Optimization, 7. Peter Lang, Frankfurt am Main, 1995. iv+416 pp. |
[11] |
V. F. Demyanov and A. M. Rubinov, Exhaustive families of approximations revisited,From convexity to nonconvexity, Nonconvex Optim. Appl., Kluwer Acad. Publ., Dordrecht, 55 (2001), 43-50.
doi: 10.1007/978-1-4613-0287-2_4. |
[12] |
B. N. Pshenichny, Convex Analysis and Extremal Problems (in Russian). Nauka, Moscow, 1980, 320 pp. |
[13] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton University Press, Princeton, N.J. 1970. |
[14] |
V. A. Roshchina, Limited exhausters and optimality conditions, Control Processes and Stability: Proceedings of the 36-th international conference of students and graduate students, Saint-Petresburg, Saint-Petrsburg State University Press, (2005), 521-524. |
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