How important is to formulate a convex optimization for a proposed algorithm?

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How important is to formulate a convex optimization for a proposed algorithm?



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.









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