International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 65-81

Nonsmooth analysis and optimization on partially ordered vector spaces

Thomas W. Reiland

Department of Statistics and Graduate Program in Operations Research, Box 8203, North Carolina State University, Raleigh 27695-8203, NC, USA

Received 21 February 1991; Revised 16 July 1991

Copyright © 1992 Thomas W. Reiland. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Interval-Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz-type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice. Sample applications to the theory of nonsmooth optimization are given.