Abstract
In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions, and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs, and η-pseudolinear programs.
| Original language | English |
|---|---|
| Pages (from-to) | 587-601 |
| Number of pages | 15 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 153 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jun 2012 |
| Externally published | Yes |
Keywords
- Dini directional derivatives
- Invariant pseudolinearity
- Invex sets
- Nonsmooth variational-like inequalities
- Pseudoinvexity
- Solution sets of a program
ASJC Scopus subject areas
- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics