
Optimization with General Attributes 251
9.2.1 Mapping to the Task Scheduling Problem
To illustrate the generality of this framework, this subsection uses the new
notation to exactly represent the task scheduling problem from Section 9.1.
For that problem, one can define the control action α[k]tohavetheform
α[k]=(c[k],m[k],I[k]), and the action space A is then the set of all (c, m, I)
such that c ∈{1,...,N}, m ∈M,and0≤ I ≤ I
max
.
The frame size is T [k]=D[k]+I[k], and
ˆ
T (α[k]) is given by:
ˆ
T (α[k]) =
ˆ
D(c[k],m[k]) + I[k]
We then define y
0
[k] as the energy expended in frame k,sothaty
0
[k]=e[k]
and ˆy
0
(α[k]) = ˆe(c[k],m[k]). There are N constraints, so define ...