CAAM 564 Homework Assignments

The problems are numbered as in the textbook.

HW 4: Due 4/xx, Tue.

Solve the 2 tent problems:

         min S(x,y,z), st. V(x,y,z) = V0, h0 <= y + z <= h1 
	 max V(x,y,z), st. S(x,y,z) = S0, h0 <= y + z <= h1

using the augmented Lagrange multiplier method. You may use matlab function fmincon.m with bound constraints only.

Also use the augmented Lagrange multiplier method to solve the LP:

         max b'*y: -1 <= A'*y <= 1.

HW 3: Due 3/17, Tue.

Solve the 2 tent problems:

         min S(x,y,z), st. V(x,y,z) = V0, y + z = h0 
	 max V(x,y,z), st. S(x,y,z) = S0, y + z = h0

where S is the surface area and V is the volume of the tent which has a square base of 2x by 2x, a height of y for the main body, and a height of z for the pyramid top. The tent does not have a bottom.

Use Newton's method to solve the KKT system. Your matlab functions for the 2 problems should have the interfaces:
```
	          [S,x,y,z,u] = Newton_tent1(V0,h0); 
 	          [V,x,y,z,u] = Newton_tent2(S0,h0); 
```
where u is the Langrange multiplier vector. You may use finite difference approximation for the Jacobian of the KKT system.
Test your codes with test_tent.m. Without your codes, you can run the test with the instructor's pcodes in pfiles.zip.

HW 2: Due 2/12, Thur.

Assignment: Primal-Dual Interior-point method for LP
Submit your output (truncated the iteration history if too long) along with your code and a short write-up (typed) explaining what you observe.
Please submit your code and the (truncated) printout from the two tests.

HW 1: Due 2/3, Tue., 2:30pm

Exercises 12.4, 12.5, 12.10, 12.17