convert_quad_constraint

convert_quad_constraint(Q, B, l, u)

convert_quad_constraint() - Convert quadratic constraints from bounded to equality/inequality pair.

[ieq, igt, ilt, Qe, Be, de, Qi, Bi, di] = convert_quad_constraint(Q, B, l, u)
[ieq, igt, ilt, Q, B, d] = convert_quad_constraint(Q, B, l, u)

Convert a set of constraints of the form:

l(j) <= x'*Q{j}*x + B(j,:)*x <= u(j),  j = 1,2,...,nq

to:

x'*Qe{j}*x + Be(j,:)*x  =  de(j),  j = 1,2,...,nqe
x'*Qi{j}*x + Bi(j,:)*x  <= di(j),  j = 1,2,...,nqi   , nq = nqe+nqi

where:

Qe = Q(ieq)
Be = B(ieq,:)
de = u(ieq)
Qi = [Q(ilt); -Q(igt)]
Bi = [B(ilt,:); -B(igt,:)]
di = [u(ilt);  -l(igt)]

Alternatively, the returned cell arrays, matrices, and RHS vectors can be stacked into a single set with the equalities first, then the inequalities.

Q = [Qe; Qi]
B = [Be; Bi]
d = [de; di]
Inputs:

  • Q (double) – \(n_q \times 1\), cell array with sparse \(n \times n\) symmetric matrices holding the quadratic parameters of the quadratic constraints

  • B (double) – \(n_q \times n\), matrix whose rows represent the linear parameters of the quadratic constraints

  • l (double) – \(n_q \times 1\), quadratic constraint lower bound vector

  • u (double) – \(n_q \times 1\), quadratic constraint upper bound vector

Outputs:

  • ieq (integer) – vector of indices of equality constraints

  • igt (integer) – vector of indices of lower bounded inequality constraints

  • ilt (integer) – vector of indices of upper bounded inequality constraints

  • Qe (double) – cell array of quadratic parameters for equality constraints

  • Ae (double) – matrix of linear parameters for equality constraints

  • de (double) – equality constraint RHS

  • Qi (double) – cell array of quadratic parameters for inequality constraints

  • Ai (double) – matrix of linear terms for inequality constraints

  • di (double) – inequality constraint RHS

  • Q (double) – stacked cell of quadratic parameters

  • B (double) – stacked constraint matrix of linear parameters

  • d (double) – stacked RHS

See also convert_constraint_multipliers().