Unformatted text preview: zero.
Instead, we will focus on the Fritz John points where there exists a set of Lagrangian
. Without loss of generality, we will require
The following optimality conditions were developed independently by Karush in 1939 and
by Kuhn and Tucker in 1951. (Note: We dropped the requirement that some is nonzero, since we have taken
̅ Geometrical Insight: We are expressing
̅ as a non-negative linear
combination of the gradients of the binding constraints.
174 g1(x) 0 g1 (x) x f (x) f ( x ) g 2 (x) g2(x) 0 Suppose that we constructed the first order (linear) approximation for this problem about
̅ That is, we replace each constraint by their linear (tangential) approximations and
ignore the non-binding constr...
View Full Document
- Fall '13
- Optimization, Mathematical optimization, KKT conditions, KKT point