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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, 10 (2011), 3. Google Scholar |
[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, (2010). Google Scholar |
[3] |
M. E. Abbasov and V. F. Demyanov, Proper and adjoint exhausters in Nonsmooth analysis: Optimality conditions,, Journal of Global Optimization, 56 (2013), 569.
doi: 10.1007/s10898-012-9873-8. |
[4] |
M. Castellani, A dual representation for proper positively homogeneous functions,, J. Global Optim., 16 (2000), 393.
doi: 10.1023/A:1008394516838. |
[5] |
V. F. Demyanov, Optimality Conditions and Variational Calculus,, (In Russian). Moscow, (2005). Google Scholar |
[6] |
V. F. Demyanov, Exhausters and convexificators - new tools in nonsmooth analysis,, Nonconvex Optim. Appl., 43 (2000), 85.
doi: 10.1007/978-1-4757-3137-8_4. |
[7] |
V. F. Demyanov, Proper Exhausters and Coexhausters in Nonsmooth Analysis,, Optimization, 61 (2012), 1347.
doi: 10.1080/02331934.2012.700929. |
[8] |
V. F. Demyanov, Exhausters of a positively homogeneous function,, Optimization, 45 (1999), 13.
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.
doi: 10.1080/02331930600815777. |
[10] |
V. F. Demyanov and A. M. Rubinov, Constructive Nonsmooth Analysis,, Approximation & Optimization, (1995).
|
[11] |
V. F. Demyanov and A. M. Rubinov, Exhaustive families of approximations revisited,From convexity to nonconvexity,, Nonconvex Optim. Appl., 55 (2001), 43.
doi: 10.1007/978-1-4613-0287-2_4. |
[12] |
B. N. Pshenichny, Convex Analysis and Extremal Problems (in Russian)., Nauka, (1980).
|
[13] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (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, (2005), 521. Google Scholar |
show all references
References:
[1] |
M. E. Abbasov, Extremality conditions in terms of adjoint exhausters,, (In Russian) Vestnik of Saint-Petersburg University; Applied mathematics, 10 (2011), 3. Google Scholar |
[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, (2010). Google Scholar |
[3] |
M. E. Abbasov and V. F. Demyanov, Proper and adjoint exhausters in Nonsmooth analysis: Optimality conditions,, Journal of Global Optimization, 56 (2013), 569.
doi: 10.1007/s10898-012-9873-8. |
[4] |
M. Castellani, A dual representation for proper positively homogeneous functions,, J. Global Optim., 16 (2000), 393.
doi: 10.1023/A:1008394516838. |
[5] |
V. F. Demyanov, Optimality Conditions and Variational Calculus,, (In Russian). Moscow, (2005). Google Scholar |
[6] |
V. F. Demyanov, Exhausters and convexificators - new tools in nonsmooth analysis,, Nonconvex Optim. Appl., 43 (2000), 85.
doi: 10.1007/978-1-4757-3137-8_4. |
[7] |
V. F. Demyanov, Proper Exhausters and Coexhausters in Nonsmooth Analysis,, Optimization, 61 (2012), 1347.
doi: 10.1080/02331934.2012.700929. |
[8] |
V. F. Demyanov, Exhausters of a positively homogeneous function,, Optimization, 45 (1999), 13.
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.
doi: 10.1080/02331930600815777. |
[10] |
V. F. Demyanov and A. M. Rubinov, Constructive Nonsmooth Analysis,, Approximation & Optimization, (1995).
|
[11] |
V. F. Demyanov and A. M. Rubinov, Exhaustive families of approximations revisited,From convexity to nonconvexity,, Nonconvex Optim. Appl., 55 (2001), 43.
doi: 10.1007/978-1-4613-0287-2_4. |
[12] |
B. N. Pshenichny, Convex Analysis and Extremal Problems (in Russian)., Nauka, (1980).
|
[13] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (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, (2005), 521. Google Scholar |
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