Perfect duality for convexlike programs

Journal of Optimization Theory and Applications - 1982
M. Hayashi1, H. Komiya2
1EDP Manufacturing and Processing Industries System Division, Nippon Electric Company, Tokyo, Japan
2Department of Information Sciences, Tokyo Institute of Technology, Tokyo, Japan

Tóm tắt

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.

Từ khóa


Tài liệu tham khảo

Duffin, R. J.,Convex Analysis Treated by Linear Programming, Mathematical Programming, Vol. 4, No. 2, 1973.

Duffin, R. J.,Lagrange Multiplier Method for Convex Programs, Proceedings of the National Academy of Science of the USA, Vol. 72, No. 5, 1975.

Borwein, J. M.,A Note on Perfect Duality and Limiting Lagrangians, Mathematical Programming, vol. 18, No. 3, 1980.

Elster, K. H., andNehse, R.,Optimality Conditions for Some Nonconvex Problems, Springer-Verlag, New York, New York, 1980.

Fan, K.,Minimax Theorems, Proceedings of the National Academy of Sciences of the USA, Vol. 39, No. 1, 1953.

Nagahisa, Y., andSakawa, Y.,Nonlinear Programming in Banach Spaces, Journal of Optimization Theory and Applications, Vol. 4, No. 3, 1969.

Rockafellar, R. T.,Conjugate Duality and Optimization, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1974.

Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.

Kelly, J. L., andNamioka, I.,Linear Topological Spaces, Springer-Verlag, New York, New York, 1963.

Thông tin
Thông tin xuất bản

Journal of Optimization Theory and Applications

Thông tin tác giả