Convex Optimization, Spring 2016
Additional Exercises 3-solution
9.6 Barrier method for LP. Consider a standard form LP and its dual
cT x
maximize
bT y
Ax = b
subject to
AT y c,
x0
with A Rmn and rank(A) = m. In the barrier method the (feasible) Newton me

Convex Optimization, Spring 2016
Homework 6
Due on 8:15a.m. May. 26, 2016, before class
Note: Please also submit your Matlab code by printing it out (use the data provided in the xx.dat and
rename them as xx.mat).
1) Distributed lasso. Consider the `1 -re

Convex Optimization, Spring 2016
Additional Exercises 4-solution
4.10 Binary least-squares. We consider the non-convex least-squares approximation problem with binary constraints
minimize
subject to
Ax b22
x2k = 1, k = 1, , n,
(1)
where A Rmn and b Rm . W

Convex Optimization, Spring 2016
Additional Exercises 1
2.20 Show that the following functions f : Rn R are convex.
(a) The difference between the maximum and minimum value of a polynomial on a given interval, as a
function of its coefficients:
f (x) = su

Convex Optimization, Spring 2016
Homework 5 solution
Due on 8:15a.m. May 12, 2016, before class
Note: Please also submit your Matlab code by printing it out (use the data provided in the appendix).
1) Barrier method for LASSO: Implement a barrier method f

Convex Optimization, Spring 2016
Homework 1 Solution
Due on 8:15a.m. Mar. 22, 2016, before class, handwritten
1. Convexity Verification:
1) Determine the convexity (i.e., convex, concave, or neither) of the following functions.
(10 points)
(a) f (x1 , x2

Convex Optimization, Spring 2016
Homework 2 Solution
Due on 8:15a.m. Mar. 31, 2016, before class
Justify all the answers. Be concise. All the notations follow the textbook. 4 problems in total.
1) Linear Regression: Given n = 50 pairs of data (xi , yi ),

Convex Optimization, Spring 2016
Homework 4 solution
Due on 8:15a.m. Apr. 21, 2016, before class
Justify all the answers. Be concise. All the notations follow the textbook. 2 problems in total.
1) GP : Rewrite the following GPs in standard form:
a) The fa

Convex Optimization, Spring 2016
Additional Exercises 4
4.10 Binary least-squares. We consider the non-convex least-squares approximation problem with binary constraints
minimize
subject to
Ax b22
x2k = 1, k = 1, , n,
(1)
where A Rmn and b Rm . We assume

Convex Optimization, Spring 2016
Homework 3 solution
Due on 8:15a.m. Apr. 7, 2016, before class
Justify all the answers. Be concise. All the notations follow the textbook. 4 problems in total.
1) Derive the dual problems of the following primal problems: