Abstract
The minimizing problem for a convex program has a dual problem, that is, the maximizing problem of the Lagrangian. Although these problems have a duality gap in general, the duality gap can be eliminated by relaxing the constraint of the minimizing problem, so that the constraint is enforced only in the limit. We extend this result to the convexlike case. Moreover, we obtain a necessary condition for optimality for minimizing problems whose objective function and constraint mapping have convex Gateaux derivative.
| Original language | English |
|---|---|
| Pages (from-to) | 179-189 |
| Number of pages | 11 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 38 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1982 Oct 1 |
| Externally published | Yes |
Keywords
- Convexlike programs
- Lagrangian function
- necessary condition for optimality
- perfect duality
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
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Cite this
Hayashi, M., & Komiya, H. (1982). Perfect duality for convexlike programs. Journal of Optimization Theory and Applications, 38(2), 179-189. https://doi.org/10.1007/BF00934081