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Generalized exhausters: Existence, construction, optimality conditions
1.  Saint Petersburg State University, Universitetskaya nab., 79, St. Petersburg, Russian Federation 
References:
[1] 
M. E. Abbasov, Extremality conditions in terms of adjoint exhausters,, (In Russian) Vestnik of SaintPetersburg University; Applied mathematics, 10 (2011), 3. 
[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). 
[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/s1089801298738. 
[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). 
[6] 
V. F. Demyanov, Exhausters and convexificators  new tools in nonsmooth analysis,, Nonconvex Optim. Appl., 43 (2000), 85. doi: 10.1007/9781475731378_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: 10.1007/9781461302872_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 36th international conference of students and graduate students, (2005), 521. 
show all references
References:
[1] 
M. E. Abbasov, Extremality conditions in terms of adjoint exhausters,, (In Russian) Vestnik of SaintPetersburg University; Applied mathematics, 10 (2011), 3. 
[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). 
[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/s1089801298738. 
[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). 
[6] 
V. F. Demyanov, Exhausters and convexificators  new tools in nonsmooth analysis,, Nonconvex Optim. Appl., 43 (2000), 85. doi: 10.1007/9781475731378_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: 10.1007/9781461302872_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 36th international conference of students and graduate students, (2005), 521. 
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