Input format

1.4 Input format

BiqCrunch solves any problem that can be stated as

( || maximize xT S0x+ sT0x { subject to xT Six+ sTi x ≤ ai, i ∈ {1,...,mI} || xT Six+ sTi x = ai, i ∈ {mI +1,...,mI +mE } ( x ∈ {0,1}n

(1.1)

where x^TS_ix + s_i^Tx is a quadratic function with integer coefficients, for i = 0,…,m_I + m_E, and a is an integer vector. The problem has to be written in BC format which uses a sparse representation, similar to the sparse SDPA format. The objective function and constraint coefficients are described as (n + 1) × (n + 1) matrices, linear terms being stored in the last line/column: Q_i = [ S si]
sTii 2
2 0 .

Some input files for BiqCrunch are provided for several problems (see section Examples).

1.4.1 Example