10 Rotated second-order Cone (socp2)

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Problem

A rotated second-order cone model contains quadratic constrainst of the form

∑
    x2 ≤ wv
 i∈I  i

where xi, v, and w are variables. These constraints are convex and they are automatically recognized and solved by Gurobi and Cplex, for example.

A small model example is given here.


Listing 8: The Complete Model implemented in LPL [10]
model socp2 "Rotated second-order Cone"; 
  set i:=1..3; 
  parameter c{i} := [11 7 9]; 
            b{i} := [ 5 6 8]; 
  variable x{i} [0..100]; r{i} [0..100]; k{i}; 
  constraint 
    A: sum{i} 2*r <= 1; 
    B{i}: k = Sqrt(b); 
    C{i}: k^2 <= 2*x*r; 
  minimize obj: sum{i} c*x; 
  Writep(obj,x,r,k); 
end