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Assume that we have a non-convex optimization $\min_{A,B} f(A,B)+\lambda g(A,B)$. Specifically, $f(A,B)+\lambda g(A,B)$ is not joint convex, but it is convex with regard to one variable when fixing another variable.

Now the question is could we use the following equation to prove the monotonic decrease of the objective $f(A,B)+\lambda g(A,B)$ value during the alternating technique based algorithm 1 like optimization process?

$$(A^{(t+1)},B^{(t+1)})=\arg \min_{A,B} f(A^{(t)},B^{(t)})+\lambda g(A^{(t)},B^{(t)}), $$

where $t$ is the iteration counter.

Algorithm-1:
Repeat
1. Updating $A^{(t+1)}$
2. Updating $B^{(t+1)}$
3. t=t+1;
Until convergence

Thank you so much for your reply.

Lia
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  • Are you talking about coordinate-wise descent? – copper.hat Mar 14 '14 at 07:25
  • Yes, but the objective is nonconvex, so we hope to depict the curve of the objective value to see whether the algorithm converges or not. Thank you. – Lia Mar 14 '14 at 09:18

0 Answers0