ISSN:
1573-2878
Keywords:
Optimization
;
necessary conditions
;
Kuhn-Tucker theorem
;
multiplier rules
;
separation of convex sets
;
mathematical programming
;
generalized derivatives
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider the following abstract mathematical programming problem: in a setD, find an element that optimizes a real function φ0, subject to inequality constraints φ1⩽0, ..., φ p ⩽0 and equality constraints φ p+1=0, ..., φ p+q =0. Necessary conditions for this problem, like the Karush-Kuhn-Tucker theorem, can be seen as a consequence of separating with a hyperplane two convex sets inR p+q+1, the image space of the map Φ=(φ0, φ1, ..., φ p+q ). This paper reviews this approach and organizes it into a coherent way of looking at necessary conditions in optimization theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00933503
Permalink
