Interior Points Method

Implementation of Interior Points Method in MATLAB (My Assignment in Linear Optimization course [MTH305] [IIIT-Delhi]).

Further, we solved the following Linear Problem:

min   1'u + 1'v
st. 
      a'xi + b >=  1 - ui      i=1..N
      a'yj + b <= -1 + vj      j=1..M
      u >= 0
      v >= 0

We were provided with:

1. DB_Vecs.npy (Sequence vectors for training)
2. DB_Labels.npy (corresponding labels)
3. Q_Vecs.npy (Test sequences)

Converted these into Matrix file - data.mat.

We were to submit the results (Labels for Q_vecs) as list/numpy array. Here, the output is in Matrix file - uk.mat.

References

1. Video Resources:

   • https://www.youtube.com/watch?v=oMRVDILkpUI - Stephen Boyd, Lecture 18, Convex Opt (discusses Barrier methods).
   • https://www.youtube.com/watch?v=StlHUwd_AgM - Stephen Boyd, Lecture 18, Convex Opt (discusses Newtons method).
   • https://www.youtube.com/watch?v=4mpq-wsYBxw - MIT Lecture on IP method (different perspective).

2. Text Resources:

   • From Stephen Boyd's book, see Chapters, 10 and 11 to 11.3
   • Specially relevant for the programming assignment are the following sections: 10.3 and 10.4

3. Proof of convergence:

   • https://simons.berkeley.edu/sites/default/files/docs/6912/steve-simons-intpt.pdf
   • http://www.seas.ucla.edu/~vandenbe/ee236a/lectures/mpc.pdf

4. Advanced: https://www.youtube.com/watch?v=7CMWdO5dgdQ