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Some calculus rules for contingent epiderivatives. (English) Zbl 1032.49021

In this paper, several calculus rules for contingent epiderivatives of set-valued maps are presented. The paper concentrates on results related to scalar multiplication, sum formulae and chain rules.

MSC:

49J52 Nonsmooth analysis
49J53 Set-valued and variational analysis
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
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References:

[1] Aubin J.P., Mathematical Analysis and Applications pp 160– (1981)
[2] Aubin J.P., Set Valued Analysis (1990) · Zbl 0713.49021
[3] DOI: 10.1023/A:1021733402240 · Zbl 0922.90118 · doi:10.1023/A:1021733402240
[4] DOI: 10.1016/0362-546X(87)90008-3 · Zbl 0639.49014 · doi:10.1016/0362-546X(87)90008-3
[5] DOI: 10.1007/s001860050021 · Zbl 0927.90095 · doi:10.1007/s001860050021
[6] DOI: 10.1080/02331938808843348 · Zbl 0655.49009 · doi:10.1080/02331938808843348
[7] DOI: 10.1137/S1052623496311697 · Zbl 1029.90065 · doi:10.1137/S1052623496311697
[8] Jahn J., Mathematical Vector Optimization in Partially Ordered Linear Spaces (1986) · Zbl 0578.90048
[9] Jahn J., Introduction to The Theory of Nonlinear Optimization (1996) · Zbl 0855.49001 · doi:10.1007/978-3-662-03271-8
[10] DOI: 10.1007/BF01217690 · Zbl 0889.90123 · doi:10.1007/BF01217690
[11] Luc D.T., Lecture Notes in Economics and Mathematical Sciences, 319, in: Theory of Vector Optimization (1988) · Zbl 0654.90082
[12] Pennanen T., J. ConvexAnal. 6 pp 235– (1999)
[13] DOI: 10.1112/plms/s3-39.2.331 · Zbl 0413.49015 · doi:10.1112/plms/s3-39.2.331
[14] Rockafellar R.T., Variational Analysis (1997) · Zbl 0932.90001
[15] DOI: 10.1090/S0002-9947-1987-0891640-2 · doi:10.1090/S0002-9947-1987-0891640-2
[16] DOI: 10.1137/0325072 · Zbl 0633.46043 · doi:10.1137/0325072
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