
163Design Optimization
2. Determine if the following optimization problems are convex or
nonconvex.
a. Maximize =fx x()
2
, subject to x − 5 ≤ 0 and
2
.
b. Minimize =++(,)
22
fxyx
y, subject to x, y > −56.
3. What are the advantages of convex functions, convex constraints,
and both in an optimization problem?
4. Solve the following linear programs using the simplex method:
a.
xx
xx
x
xx
subjectt
3
12
12
1
12
≤
≥
b.
xx
x
xxx
xx
xxxx
subjectt
6
15
3
,,
124
13
4
123
34
1 234
+≤
≤
++≤
−≤
≥
5. What are interior point methods in optimization?
6. Solve the following optimization problems using KKT conditions:
a.
fx xx
gx ...