How CVX solves the maximum value of the difference between two concave functions?

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How CVX solves the maximum value of the difference between two concave functions?

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CVX does not do this automatically for you. You can apply Difference of Convex Programming (convex-concave procedure) https://web.stanford.edu/~boyd/papers/pdf/cvx_ccv.pdf .

cvxpy can apply this automatically. using the DCCP extension https://github.com/cvxgrp/dccp

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Can matlab solve the problem of calculating the maximum value of concave function minus concave function?

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This can’t be done automatically in any MATLAB tool I am aware of. However, CVX can be used to implement the convex-concave procedure described in the ffrst link. Note that maximizing concave minus concave is basically the same as minimizing convex minus convex, accomplished by negating the objective function.

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