Min function in objective problem

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How can I convert this Min function (bold highlighted) in objective problem into simple mathematical equation:


Min(x,y)⁡[a[i]*(x[i]-y[i])+ b[i] min⁡(x[i], M-c[i])] s.t. c[i]-x[i]+y[i]≤M

here x[i] and y[i] are decision variables.