General mixed-integer quadratically constrained problem instances

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Problem Description

Files format

The instances files

A few references where these instances are used

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Problem description

This library contains instances of quadratically constrained Mixed Integer Quadratic Programs (MIQCP_m) that can be formulated as follows:

		Min	f(x) = xt Q0 x + ct x
(MIQCPm)		s.t.	xt Qr x + c r t x = bqr r=1, ..., mq : mq quadratic equalities xt Qr x + c r t x ≤ bqr r=mq+1, ..., (mq+pq) : pq quadratic inequalities 0 ≤ ℓ ≤ x ≤ u n positive and lower and upper bounded variables xi ∈ N i=1,..,nb_int integer variables xi ∈ R i=nb_int,...,n real variables

Where Q_r ∈ S_n, c_r ∈ Rⁿ, bq ∈ R^mq+pq, ℓ ∈ Rⁿ, and u ∈ Rⁿ. In these instances, for all r= 0, ..., mq+pq, the submatrix of pure real quadratic terms of each matrix Q_r defined by (q_{(rij) ∈ {nb_int..n}x{nb_int..n}} is positive semidefinite.

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Files format  

Each .dat file contains one instance, in the format of solver SMIQCP:

n nb_int 0 0 mq pq
u
u₁, u₂... u_n
ℓ
ℓ₁, ℓ₂... &ell_n
Q
nnzQ₀
i j q_0ij
C
nnzc₀
i c_0i
Aq
nnzQ_r + nnzc_r r=1..mq
r 0 i+1 c_ri
r i+1 j+1 q_rij
bq
nnzb_r r=1..mq
r i b_ri
Dq
nnzQ_r + nnzc_r r=1,..,pq
r 0 i+1 c_ri
r i+1 j+1 q_rij
eq
nnze_r r=1..pq
r i e_ri
where nnzM is the number of non zero elements of matrix/vector M.

An example is available here  

The optimal solution values are reported here :

class IQCP₁  

class IQCP₅  

class IQCP₀  

class MIQCP₁  

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The IQCP-MIQCP instance files  

A convex instance  

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References

[1] S. Elloumi and A. Lambert. Global solution of non-convex quadratic=ally constrained quadratic programs Optimization Methods and Software 34 (1): 98-114, (2019) DOI: 10.1080/10556788.2017.1350675

[2] A. Billionnet, S. Elloumi and A. Lambert. Exact quadratic convex reformulations of mixed-integer quadratically constrained problems Mathematical Programming serie A. 158 (1), 235-266 (2016) DOI: 10.1007/s10107-015-0921-2

[3] A. Billionnet, S. Elloumi and A. Lambert. Convex reformulations of Integer Quadratically Constrained Problems, ISMP (21th International Symposium of Mathematical programming), Berlin, Germany, august 19-24, 2012.

[4] A. Billionnet, S. Elloumi and A. Lambert. A solution method for quadratically constrained integer problems. Optimization 2011, Lisbon, july, 2011.

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