What are some recent advances in non-convex optimization research?

What are some recent advances in non-convex optimization research? originally appeared on Quora – the knowledge sharing network where compelling questions are answered by people with unique insights. Answer by Anima Anandkumar, Faculty at UC Irvine, Machine learning researcher, on Quora. Non-convex optimization is now ubiquitous in machine learning. While previously, the focus was on convex relaxation methods, now the emphasis is on being able to solve non-convex problems directly. It is not possible to find the global optimum of every non-convex problem due to NP-hardness barrier. An alternate approach is: when can it be solved efficiently (preferably in low order polynomial time). Recent theoretical work has established that many non-convex problems can be solved near-optimally, but simple iterative algorithms, e.g. gradient descent with random restarts. The conditions for success…


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