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Homework
10 (by May 19, 2009):
Make lecture notes
of opt16b_17.avi,
and solve examples suggested there for home consideration
Homework
9 (in MATLAB) on Constrained
Optimization (by May
26, 2009)
1. Create 2D constrained optimization problem with two active and one
inactive inequality constraints,
such that the optimal solution x* is known. Use quadratic and linear
functions as the objective and the constraints.
2. Knowing the optimal solution x*, solve KKT linear system and find
the optimal Lagrange Multipliers
3. Derive the dual problem
4. Solve the original (primal) problem with the Augmented Lagrangian method
using Newton
method for inner optimization.
Create 4 semilogy subplots showing how the following quantities change with
global Newton iterations (X-axis shows total count of Newton iterations
over all unconstrained inner optimizations):
a) Gradient of the Augmented Lagrangian aggregate
b) Maximal constraint violation
c) Residual in the objective function |f(x) -f(x*)|
d) Distance to the optimal point ||x -x*|| and to the optimal multipliers ||lambda –
lambda*||
5. Solve the dual problem with the Augmented Lagrangian method and
verify that it's solution coincides with Lagrange multipliers provided
by pp 2 and 4
You can use interface similar to Constrained GUI Code, see also Constrained GUI tutorial
Good luck!
Homework
8 (by May 12, 2009):
Make lecture notes
of opt15.avi and opt16.avi, and solve examples suggested
there for home consideration
Homework
7 (by May 5, 2009):
Make lecture notes
of opt13.avi and opt14.avi, and solve examples
suggested there for home consideration
Now,
due to Oded, we have Discussion Group http://groups.google.com/group/tech_opt_09?hl=en
Homework
6 - in MATLAB (by May 5, 2009):
Implement
Quasi-Newton BFGS with inexact line search in MATLAB, and test it with the
same functions as you did before
With
gradient descent and Newton.
By
request of the students HW4 is also postponed to May 5.
Homework
5 (by April 26, 2009):
Make lecture notes
of opt11.avi
and opt12.avi,
and solve examples suggested there for home consideration
Some students have technical problems with GUI for
unconstrained optimization. You can
just build your code with the interface similar to fminunc.m , without
GUI
The missed lecture from March 24 will be accomplished on Sunday,
April 26, 16:30
, room, as usual, TAUB-201
New Literature links added: Linear Algebra and Scientific Computing
video lectures from MIT
Homework 4 - MATLAB
exercise (by April 26, 2009):
1-2. Implement Gradient Descent method and Newton method based
on Modified Cholesky
Factorization.
Use Armijo inexact line
search.
You can use the Unconstrained
GUI Code (see Unconstrained
GUI tutorial), or build your code with the interface
similar to fminunc.m from the MATLAB Optimization Toolbox.
3. Build an universal
Matlab function which tests user's
gradient/Hessian evaluation function via finite differences
4. Test your code with your own well- and ill-conditioned quadratic and non-quadratic problems
Show linear/quadratic convergence of function
values/gradients on logarithmic scale
(use semilogy plot command; remember to subtract optimal
function value before plotting
function convergence)
Remark: One of the recommended non-quadratic problems - Rosenbrock function,
See
also http://www.kyb.tuebingen.mpg.de/bs/people/carl/code/minimize/rosenbrock.m
:
f(x) = sum_{i=1:N-1} 100*(x(i+1) - x(i)^2)^2 + (1-x(i))^2 where N is the dimension of x. The true minimum is 0 at x = (1 1 ... 1).
Homework
3 (by April 21, 2009):
Make lecture notes of opt09.avi and
opt10.avi,
and solve examples suggested there for home consideration
Homework
2: make lecture notes of opt06_new_compress.avi,
opt07.avi
(starting from 13 min 15 sec point),
and opt08.avi
, and solve examples suggested there
for home consideration (note that these lectures have almost no home
examples). Be ready to present this work
at the next lecture on April
7, 2009
Homework
1: a) make lecture notes of the
lectures 1 – 5
b) solve examples
suggested there for home consideration
Be ready to present this work at the next lecture on April 7, 2009
There
will be no lecture on March
24, 2009. Tentatively, it
will be accomplished on Sunday, April 26, 16:30
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