Consider an optimization problem,
minimize f(Ax)+x^T x
the variable is n-vector x. The matrix A has size m by n and rank m. f is not necessarily differentiable or convex.
Show that the problem can be formulated as an equivalent problem with m variables, by making change of y = Ax.
Thanks.
DEar Kko,
I suggest for you a link and attached files in topics.
Can simplex method solve non-convex optimization problem?
math.stackexchange.com/.../can-simplex-method-solve-non-conve...
Best regards
These following additional links may be usefull:
https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiC-YGF_NDRAhVHbxQKHQIMAFoQFgghMAA&url=https%3A%2F%2Fwww.lix.polytechnique.fr%2F~liberti%2Farschapter.pdf&usg=AFQjCNHvqnWA6hMmPYQZqPNQIkJ8D1zg5g
http://booksc.org/dl/7952235/f0c2ff
http://www.ifp.illinois.edu/~angelia/nonnegative_augmenting_final_revised.pdf
http://booksc.org/dl/3335407/206739
https://arxiv.org/pdf/1212.6492v1.pdf
http://www.academia.edu/download/30839134/coa08.pdf
Dear Kko,
As suggested by Mohamed-Mourad Lafifi, the normal simplicial algorithm combined with a concave optimization approach may be of interest to solve your optimization problem. Follow these links:
- Section §4 issued from http://www.cv-foundation.org/openaccess/content_cvpr_2014/papers/Lian_Point_Matching_in_2014_CVPR_paper.pdf
- http://www4.comp.polyu.edu.hk/~cslzhang/paper/conf/RPM_concave_ecv12.pdf
- https://ia800207.us.archive.org/16/items/springer_10.1007-978-3-662-03199-5/10.1007-978-3-662-03199-5.pdf
Best regards
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix