A note on perfect duality and limiting lagrangeans
- 63 Downloads
In this note we derive and extend the substance of recent results on Perfect Duality and Limiting Lagrangeans by using standard convex analysis and convex duality theory.
Key wordsLimiting Lagrangean Duality Gaps Perfect Duality Convex Conjugates Convex Duality Semi-infinite Programs Closure
Unable to display preview. Download preview PDF.
- A. Charnes, W.W. Cooper and K.O. Kortanek, “Duality in semi-infinite programs and some works of Haar and Caratheodory”,Management Science 9 (1963) 209–229.Google Scholar
- C.E. Blair, J. Borwein and R.G. Jeroslow, “Convex programs and their closures”, Management Science Series, GSIA, Carnegie—Mellon University, and Georgia Institute of Technology (September 1978).Google Scholar
- R.J. Duffin, “Convex analysis treated by linear programming”,Mathematical Programming 4 (1973) 125–143.Google Scholar
- R.J. Duffin and L.A. Karlovitz, “An infinite linear program with a duality gap”,Management Science 12 (1965) 122–134.Google Scholar
- R.J. Duffin and R.G. Jeroslow, “Lagrangean functions and affine minorants”, Preliminary Report (November 1978).Google Scholar
- I. Ekeland and R. Temam,Convex analysis and variational problems (North-Holland, Amsterdam, 1976).Google Scholar
- R.G. Jeroslow, “A Limiting Lagrangean for infinitely-constrained convex optimization inR n”, Management Science Research Report no. 417r, GSIA, Carnegie—Mellon University (April 1978 revised June and July 1978).Google Scholar
- K.O. Kortanek, “Constructing a perfect duality in infinite programming”,Applied Mathematics and Optimization 3 (1977) 357–372.Google Scholar
- J.L. Kelley and I. Namioka,Linear topological spaces (Springer-Verlag, New York, 1963).Google Scholar
- R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, NJ, 1970).Google Scholar
© The Mathematical Programming Society 1980