I have tried many initial points, but the first step always fails and the rest steps are normal(solved or inaccurate/solved). Does it matter if only the first step fails?
MOSEK can solve your problem without using the successive approximation method. Using Mosek should be faster and more robust in this case.
Follow @Erling’s advice if you have access to Mosek.
As for the Successive approximation method, what matters is the final status reported by CVX.Don’t worry about the intermediate output for the Successive approximation method.
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