Homework #1

sedumi

Kolman & Beck, Ch.1 Eg.1
: Activity Analysis or Product Mix

>> c = [-120; -100; 0; 0];
>> A = [ 2, 2, 1, 0; 5, 3, 0, 1];
>> b = [8, 15];
>> x= sedumi(A,b,c)
SeDuMi 1.1R3 by AdvOL, 2006 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 2, order n = 5, dim = 5, blocks = 1
nnz(A) = 6 + 0, nnz(ADA) = 4, nnz(L) = 3
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            4.18E-002 0.000
  1 : -5.02E+002 1.25E-002 0.000 0.2989 0.9000 0.9000   1.77  1  1  3.8E+000
  2 : -4.29E+002 3.65E-003 0.000 0.2927 0.9000 0.9000   2.52  1  1  6.4E-001
  3 : -4.29E+002 2.84E-004 0.000 0.0778 0.9900 0.9900   1.19  1  1  4.5E-002
  4 : -4.30E+002 9.99E-007 0.000 0.0035 0.9990 0.9990   1.03  1  1 
iter seconds digits       c*x               b*y
  4      0.2   Inf -4.3000000000e+002 -4.3000000000e+002
|Ax-b| =  2.3e-015, [Ay-c]_+ =  0.0E+000, |x|= 2.9e+000, |y|= 3.6e+001

Detailed timing (sec)
   Pre          IPM          Post
3.125E-002    1.563E-001    0.000E+000   
Max-norms: ||b||=15, ||c|| = 120,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 2.11427.
x =
   (1,1)       1.5000
   (2,1)       2.5000
>>

hw1_1.m

hw1_1.txt

Kolman & Beck, Ch.1 Eg.3
: The Transportation Problem

>> c = [5; 7; 9; 6; 7; 10; 0; 0; 0; 0; 0];
>> A = [1,1,1,0,0,0,1,0,0,0,0; 0,0,0,1,1,1,0,1,0,0,0; 1,0,0,1,0,0,0,0,-1,0,0; 0,1,0,0,1,0,0,0,0,-1,0; 0,0,1,0,0,1,0,0,0,0,-1];
>> b = [120; 140; 100; 60; 80];
>> x = sedumi(A,b,c)
SeDuMi 1.1R3 by AdvOL, 2006 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 5, order n = 12, dim = 12, blocks = 1
nnz(A) = 17 + 0, nnz(ADA) = 17, nnz(L) = 12
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            3.24E+003 0.000
  1 :  1.16E+003 9.69E+002 0.000 0.2991 0.9000 0.9000   2.37  1  1  1.6E+000
  2 :  1.63E+003 2.05E+002 0.000 0.2114 0.9000 0.9000   1.34  1  1  3.0E-001
  3 :  1.69E+003 3.84E+001 0.000 0.1875 0.9000 0.9000   1.20  1  1  5.1E-002
  4 :  1.70E+003 1.08E+000 0.000 0.0282 0.9900 0.9900   1.03  1  1 
iter seconds digits       c*x               b*y
  4      0.5  15.9  1.7000000000e+003  1.7000000000e+003
|Ax-b| =  5.6e-014, [Ay-c]_+ =  7.6E-016, |x|= 1.1e+002, |y|= 1.4e+001

Detailed timing (sec)
   Pre          IPM          Post
3.125E-001    4.531E-001    1.250E-001   
Max-norms: ||b||=140, ||c|| = 10,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
x =
   (1,1)      68.6083
   (3,1)      51.3917
   (4,1)      31.3917
   (5,1)      60.0000
   (6,1)      28.6083
   (8,1)      20.0000

hw1_2.m

hw1_2.txt