X - UWSpace - University of Waterloo

series of upper bounak on the optimal value of P.
Roof : Since - & is a restriction of the whole problem P and the feasible ~gions of successive
subproblems - S& include that of previous subproblems at each iteration by inclusion of another
k- 1 k 0
positive variables. À, . it gives - l - 5. .. < - :, < .
-
Similady. SD: is a restriction of the dual of the whole problem P and it is lwsened ût
-
each itention by inclusion of another positive variable, pi:-'. so the feasible region of SD: gets
- - -
f bigger at each iteration. It provides that :' 5 ;: S.. . 5 ;
'
a :; . so proves the theorem.