I would like to know what the difference between the Matlab Optimization Toolbox and CVX, which is a convex optimization toolbox? Can a convex optimization problem be solved in both?
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Some differences:
- Matlab optimization toolbox is priced at $1,150. CVX is free.
- Matlab optimization toolbox implements a variety of general-purpose algorithms, beyond convex programming. CVX, as the name suggests, is restricted to convex programming. Moreover, its enforcement of disciplined convex programming means one can't just type in a formula for convex function: the user has to understand the reason for convexity and be able to demonstrate it to the program. Some beginning users find this difficult, as you can see from CVX questions asked at Computational Science.SE.
If convex optimization is all you need, 1 probably outweighs 2.