I need your help in solving the following problem:
First of all, my aim is given the objective function of logistic regression, my aim is to find the farthest point p along a direction q such that g( p ) = 1 which gives the following optimization problem:
variable p( d );
maximize(f( p ));
g( p ) <=1;
% d is the dimension
where g( p ) = norm(p(1:end-1),2) + 1/N * sum(log(exp(-Y.Xp) + 1)) and f( p ) = dot(p,q) for some given direction q, mostly a unit vector!
The problem is that when i run the optimization on logistic regression, it fails while on other objective function like SVM, it works fine!
The data that i use is just a data randomly sampled from a logistic distribution, as well as randomly choosing -1,+1 for each point as it’s label.
Bellow i have attached the progress done by CVX optimization tool:
Successive approximation method to be employed.
For improved efficiency, SDPT3 is solving the dual problem.
SDPT3 will be called several times to refine the solution.
Original size: 6005 variables, 2005 equality constraints
2000 exponentials add 16000 variables, 10000 equality constraints
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
2000/2000 | 8.000e+00 1.986e+02 1.184e+02 | Solved
1944/1988 | 8.000e+00 7.283e+01 4.932e+01 | Solved
281/320 | 2.936e+00 2.576e-01 1.621e-01 | Inaccurate/Solved
2/ 44 | 4.957e-05 3.842e-02 3.691e-02 | Inaccurate/Solved
28/133 | 1.838e+00 1.095e+00 1.094e+00 | Solved
118/118 | 8.000e+00 1.231e+01 0.000e+00 | Inaccurate/Solved
96/178 | 8.000e+00 1.650e+01 4.920e-01 | Solved
109/237 | 8.000e+00 2.562e+01 6.209e-01 | Inaccurate/Solved
116/116 | 8.000e+00 3.373e+01 0.000e+00 | Inaccurate/Solved
121/121 | 8.000e+00 4.335e+01 0.000e+00 | Inaccurate/Solved
109/259 | 8.000e+00 4.956e+01 8.309e-01 | Inaccurate/Solved
104/280 | 2.627e+00 5.400e+01 1.321e+00 | Solved
121/121 | 2.387e-05 6.215e+01 0.000e+00 | Inaccurate/Solved
117/117 | 9.014e-06 6.050e+01 0.000e+00 | Solved
121/121 | 9.037e-06 6.217e+01 0.000e+00 | Inaccurate/Solved
86/181 | 1.724e-04 5.566e+01 7.251e-01 | Solved
117/117 | 3.327e-05 6.050e+01 0.000e+00 | Inaccurate/Solved
121/121 | 8.779e-06 6.195e+01 0.000e+00 | Inaccurate/Solved
117/117 | 8.779e-06 6.051e+01 0.000e+00 | Inaccurate/Solved
121/179 | 7.823e-06 5.987e+01 8.343e-02 | Inaccurate/Solved
121/121 | 8.393e-06 6.194e+01 0.000e+00 | Inaccurate/Solved
121/121 | 1.986e-08 6.193e+01s 0.000e+00 | Inaccurate/Solved
92/287 | 2.093e-04 5.717e+01 3.017e+00 | Solved
117/280 | 6.313e-05 6.176e+01 7.350e-01 | Inaccurate/Solved
99/142 | 9.051e-05 6.029e+01 1.346e-01 | Solved
Optimal value (cvx_optval): NaN
All this was done under MATLAB environment.
Please advise and thanks in advance.