
148 Decision Based Design
−
5, 5[1, )
, which can be rewritten as the interval
1, 5 .
This implies that the problem requires minimization of a convex
function over a convex set and is therefore a convex optimization
problem.
2. Since f is a function of more than one variable, we need to check
the Hessian of the function for positive definiteness to determine
convexity. The Hessian is given by
−
−
12
which is positive definite. Since the feasible set is also a convex
set, the problem is a convex optimization problem.
5.3.1.2 Utility Maximization as a Convex Optimization Problem
In Chapter 3, we learned that most decision makers ...