Minimizing over the minimum of a function in linear programming -

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how can minimize function, contains inner minimum. below example. understand can start defining new variable x4=min(c1*x1, c2*x2, c3*x3), add new constraints x4<=c1*x1, x4<=c2*x2, x4<=c3*c3. not correct because x4 smaller terms above not minimum of them(actually x4 smaller minimum satisfy constraints above). how should reformulate make correct? thank you. 

minimize     (c1 * x1) + (c2 * x2) + (c3 * x3) + (c4 * min(c1*x1, c2*x2, c3*x3))  subject     #some arbitrary linear constraints:     x1 >= ...     x1 + 2*x2 <= ...      x3 >= ...     x1 + x3 == ...


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