### 11 A NQCP model (bilinear)

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Problem

All models with quadratic constraints seen so far are convex: QP, QPC, SOCP.

Models with only linear and quadratic terms which are non-convex are called NQCP models
in LPL. They are much harder to solve, but Gurobi has a way to solve them (the parameter
“nonconvex” must be set to 2).

A small example is this model from the Gurobi model library

Listing 9:
The
Complete
Model
implemented
in
LPL
[10] model bilinear "A NQCP model";

variable x; y; z;

maximize obj: x;

constraint

A: x + y + z <= 10;

B: x * y <= 2; --(bilinear inequality)

C: x * z + y * z = 1; --(bilinear equality)

// x, y, z non-negative (x integral in second version)

Writep(obj,x,y,z);

end