Various solvers

Hi there,
There are many solvers available, such as SCS, ECOS, CLARABEL, MOSEK, etc. What are your primary factors to consider when choosing the right solver for your problem?

If you use CVX 2.2, the solver options are limited. Only Mosek and ECOS are available from among those you mentioned. Mosek will generally perform the best and can handle binary or integer problems (except for binary or integer SDP), but is not a free solver. Gurobi is another good (not free) solver available under CVX, but can not (attempt to) handle SDP problems; and the CVX interface might not work with current versions of Gurobi. SeDuMI and SDPT3 are free solvers bundled with CVX and can handle all problem type s CVX can handle, with the exception of binary or integer., but are less robust than Mosek and don’t provide the diagnostics Mosek does.

If you want access to a greater range of solvers than CVX provides, consider using YALMIP.

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What makes the MOSEK so unique? And better than ECOS?

Mosek and Gurobi are actively professionally developed and maintained, while the others are not. I will defer to Mosek people to provide more specifics if they wish.

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you find computational evidence that Mosek is faster and more stable than ECOS.

ECOS is the result of a ph.d. and to the best of my knowledge, the author is no longer involved and very little active development of the code is happening. Mosek is also the result of a ph.d. but has been under active commercial development by the author and a whole team for 25 years.

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