-1

I proposed a new sparse coding algorithm which has goods results compared to the baselines, however, it has a non-convex optimization framework. I solved the problem using a general solver (e.g. Matlab), and although the solution is local optimum, it is still better than other relevant approaches. So how important is to formulate the problem in a convex setting? especially for publishing the work.

Bob
  • 137
  • 7
  • Can you guarantee convergence to valid solution in all cases? – Mauricio Cele Lopez Belon Jul 26 '18 at 11:48
  • @MauricioCeleLopezBelon In converges in practice, but I need to check a few things before mathematically guarantee that. So, do you mean it could be enough if i mathematically guarantee the convergence of the method? – Bob Jul 26 '18 at 11:54
  • 1
    Convergence at least should be guaranteed. Then, validity of solutions should be characterized. Cases where local minima gives good and poor results are obtained are of interest as well as pathological cases, so users can diminish or avoid poor results in some way. With that provided a method is well understood and can be accepted for publication in my opinion. – Mauricio Cele Lopez Belon Jul 26 '18 at 12:55
  • @MauricioCeleLopezBelon I think, part of the above concerns can be answered based on the method one selected for the optimization as the problem is non-convex. So, maybe i need to use a solver for which more information is available regarding its mathematical structure and its convergence behavior. – Bob Jul 26 '18 at 13:36
  • Sure, numerical method selected is of central importance. – Mauricio Cele Lopez Belon Jul 26 '18 at 14:13

1 Answers1

1

To give an answer to this question. It is true that a convex is desirable, but it is not a necessary condition for a method or algorithm to be successful or be publicable.

Non-convex problems are usually hard to treat. Slow convergence (if any) along with local minima and pathological cases are hard to avoid. However science still advance because in practice real world cases are not as pathological as may appear. If you can provide certain guarantees such as:

  • Convergence for all valid input: characterize what is a valid input for which convergence is guarantee. Numerical method used is of paramaunt importance since convergence can be assured by numerical method.

  • Characterization of solutions: what are the best and worst conditions that lead to good and poor results. Pathological cases should be also characterized.

Then your method is pretty publishable (as you can check reviewing literature).

Convex problems address the convergence requirements and numerical methods are well known and optimal. But regarding characterization of solutions you need to provide the same analysis.

Mauricio Cele Lopez Belon
  • 1,422
  • 1
  • 7
  • 9