Originally posted by: duyuquan2006

Hi,
I recently work on a mixed-integer second order cone program (MISOCP) problem, which has two objectives. I tried to construct the pareto efficient frontier via the epsilon-constraint method. Howerver, I encountered the computation difficult in calculating the nadir point. In detail, consider the problem
min z1, min z2 (1)
s.t. LP/SOCP constraints.
I first calculated the minimum of z1 and z2, and this yielded z1*,z2*; then I calculated the nadir point (z1_nadir)as
min z1
s.t. LP/SOCP constraints; (2)
z2=z2*;
And I found it was too time-consuming, and I could not find z1_nadir in 5 hours(a preset time limit).

I guess it's result from the fact "z2=z2*" is a too strong constraint which cannot easily be satisfied, for my MISOCP problem(the branch-and-bound makes it worse).

could you give me some suggestions, for calculating the nadir values?

Many thanks.
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