Abstract
We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina, The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples (this journal)]. Calculus rules for the directed subdifferentials of sum, product, quotient, maximum and minimum of quasidifferentiable functions are derived. The relation between the Rubinov subdifferential and the subdifferentials of Clarke, Dini, MichelPenot, and Mordukhovich is discussed. Important properties implying the claims of Ioffe's axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 1058-1073 |
| Number of pages | 16 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 75 |
| Issue number | 3 |
| DOIs | |
| State | Published - Feb 2012 |
Keywords
- Differences of sets
- Directed sets
- Directed subdifferential
- Quasidifferentiable functions
- Rubinov subdifferential
- Subdifferentials
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics