Abstract
We prove that for a large class of convex and lower semi-continuous biavariate functions defined over RN, epi-convergence in one variable implies epi-convergence in both variables. We also show that for closed-valued and graph-convex mappings with domains with non empty interiors, pointwise convergence implies graph convergence. We provide a number of applications for both results.
| Original language | English |
|---|---|
| Pages (from-to) | 197-208 |
| Number of pages | 12 |
| Journal | Journal of Convex Analysis |
| Volume | 11 |
| Issue number | 1 |
| State | Published - 2004 |
Keywords
- Convex functions
- Differential inclusions
- Epi-convergence
- Graph convergence
- Graph-convex mappings
- Parametric optimization
ASJC Scopus subject areas
- Analysis
- General Mathematics