Special thanks to Aubin for providing the excellent answer.
Before we go further, we need to make something very clear. There is no reference in the statement of the
problem about the sales of these mixtures. I am going to assume that the demand for these
Optimization
Homework 10
Aubin R. K. Whitley
November 12, 2008
Exercise 1 Use duality to check if x = (1, 0, 1, 0) is an optimal solution of the following linear program.
min
s.t.
x1 + 2x2 x3 x4
x1 + x2 x3 + 2x4 2
x1 + 2x2 x3 + x4 = 0
x1 x2 x3 x4 2
x1 , x
Fall 2015 EN.550.661: Nonlinear Optimization I Instructor: Daniel P. Robinson
1
EN.550.661: Nonlinear Optimization I: Review
1
Homework I
1.1
Excersice
Compute f 0 (x), f (x), 2 f (x), for the following functions f : R2 R.
(a) f (x) = 12 xT Hx, where H Rn