Maximizing L1 norm

[M.T]

Given a vector x, the objective is to maximize it's L1-norm over some convex subset C, i.e.

Objective = -norm(x,1)
Constraints =[X \in C]

Is it possible to convert this problem to linear programming?

Please advise and thanks in advance.

[Johan Löfberg]

No, the objective is nonconvex and yalmip will derive a milp (assuming C is LP-representable of course)

[M.T]

I see. I was afraid of having such a thing. So there is no way to maximize the L1 norm using any known techniques (using quadratic optimization, linear programming...) ?
The objective was minus because in YALMIP, everything is solved using minimization, and in order to get maximization, i negated the term ||x||_1.

[Johan Löfberg]

nope, intrinsically nonconvex, just think of max |x| subject to -1<=x<=1 which has two disjoint maximizers