def solveLSQ(b, A, B, bxl, bxu, bcl, bcu):
"""
Solves a constrained linear least squares problem
minimize 2-norm (A*x-b)^2
subject to bcl <= B*x <= bcu
bxl <= x <= bxu
"""
(n, m) = A.shape
q = numpy.zeros(m + n)
q[m:m + n] = 1
C1 = numpy.hstack((A, -numpy.eye(n, n))) # A*x - I*u = [A, -I]*[x;u]
C2 = numpy.hstack((B, numpy.zeros((B.shape[0], n))))
qp = QuadraticObjectiveProgram(Q=numpy.diag(v=q, k=0),
p=numpy.zeros(n + m),
A=numpy.vstack((C1, C2)))
qp.lp.bc.lower = numpy.concatenate((b, bcl))
qp.lp.bc.upper = numpy.concatenate((b, bcu))
qp.lp.bx.lower = numpy.concatenate((bxl, -numpy.inf * numpy.ones(n)))
qp.lp.bx.upper = numpy.concatenate((bxu, +numpy.inf * numpy.ones(n)))
return qp.solve()[0][0:m]
def solveLASSO(b, A, B, bxl, bxu, bcl, bcu, tau):
"""
Solves a constrained linear least squares problem
minimize 2-norm (A*x-b)^2 + tau 1-norm(x)
subject to bcl <= B*x <= bcu
bxl <= x <= bxu
"""
(n, m) = A.shape
q = numpy.zeros(2 * m + n) #[x,z,t]
q[m:m + n] = 1
C1 = numpy.hstack((A, -numpy.eye(n, n), numpy.zeros((n, m)))) # A*x - I*u = [A, -I]*[x;u]
C2 = numpy.hstack((B, numpy.zeros((B.shape[0], n + m))))
E = numpy.eye(m, m)
C3 = numpy.hstack((E, numpy.zeros((m, n)), -E))
C4 = numpy.hstack((-E, numpy.zeros((m, n)), -E))
qp = QuadraticObjectiveProgram(Q=numpy.diag(v=q, k=0),
p=numpy.concatenate((numpy.zeros(n + m), tau * numpy.ones(m))),
A=numpy.vstack((C1, C2, C3, C4)))
qp.lp.bc.lower = numpy.concatenate((b, bcl, -numpy.inf * numpy.ones(2 * m)))
qp.lp.bc.upper = numpy.concatenate((b, bcu, numpy.zeros(2 * m)))
qp.lp.bx.lower = numpy.concatenate((bxl, -numpy.inf * numpy.ones(n + m)))
qp.lp.bx.upper = numpy.concatenate((bxu, +numpy.inf * numpy.ones(n + m)))
return qp.solve()[0][0:m]
def solveQPobj(c, A, Q, bxl, bxu, bcl, bcu):
"""
Solves a convex program with a quadratic objective
maximize c'*x - (1/2) x'*Q*x
subject to bcl <= A*x <= bcu
bxl <= x <= bxu
"""
qp = QuadraticObjectiveProgram(Q=Q, p=-c, A=A)
qp.lp.bc.lower = bcl
qp.lp.bc.upper = bcu
qp.lp.bx.lower = bxl
qp.lp.bx.upper = bxu
return qp.solve()[0]
