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 |
| Externally published | Yes |
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Keywords
- Convexlike programs
- Lagrangian function
- necessary condition for optimality
- perfect duality
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics
- Management Science and Operations Research
Cite this
Perfect duality for convexlike programs. / Hayashi, M.; Komiya, Hidetoshi.
In: Journal of Optimization Theory and Applications, Vol. 38, No. 2, 10.1982, p. 179-189.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Perfect duality for convexlike programs
AU - Hayashi, M.
AU - Komiya, Hidetoshi
PY - 1982/10
Y1 - 1982/10
N2 - 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.
AB - 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.
KW - Convexlike programs
KW - Lagrangian function
KW - necessary condition for optimality
KW - perfect duality
UR - http://www.scopus.com/inward/record.url?scp=0020193048&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0020193048&partnerID=8YFLogxK
U2 - 10.1007/BF00934081
DO - 10.1007/BF00934081
M3 - Article
AN - SCOPUS:0020193048
VL - 38
SP - 179
EP - 189
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 2
ER -