Cvxpy: OSQP solver: Problem contains unspecified parameters.

[ShreyasFadnavis]

def _lstsq_initial(self, z):
        fodf_sh = csd._solve_cholesky(self._P, z)
        s = np.dot(self._reg, fodf_sh)
        fodf_sh_ = cvx.Variable(fodf_sh.shape)
        fodf_sh_.value = fodf_sh
        s_ = cvx.Variable(s.shape)
        s_.value = np.clip(s, 1e-10, None)
        init = {'x': fodf_sh_,
                's': s_}
        return init

def __init__(self, X, reg):

        # self._P_init = np.dot(X[:, :N].T, X[:, :N])
        self._P = P = np.dot(X.T, X)
        self._X = X

        # No super res for now.
        assert _rank(P) == P.shape[0]

        self._reg = reg

        # Make cvxpy matrix types for later re-use.
        self._P_mat = cvx.Parameter(P.shape)
        self._P_mat.value = P
        self._x_mat = cvx.Parameter(P.shape[0], 1)
        self._reg_mat = cvx.Parameter(reg.shape)
        self._reg_mat.value = -reg
        self._h_mat = cvx.Parameter(reg.shape[0], 1)
        h_ = np.zeros((reg.shape[0]))
        self._h_mat.value = h_

def __call__(self, signal):
        z = np.dot(self._X.T, signal)
        init = self._lstsq_initial(z)
        z_mat = cvx.Variable(z.shape[0], 1)
        z_mat.value = z
        constraints = [self._reg_mat * self._x_mat >= self._h_mat]
        objMin = cvx.Problem(cvx.Minimize(0.5 * cvx.quad_form(self._x_mat, self._P_mat) + \
                                         (z_mat.T * self._x_mat)), constraints)
        r = objMin.solve(solver=cvx.OSQP)
        fodf_sh = r['x']
        fodf_sh = np.array(fodf_sh)[:, 0]
        return fodf_sh

I am constructing the OSQP problem as above but am getting the error: 'Problem contains unspecified parameters'. Does this mean that the quad_form has been written wrongly with 2 parameters?

I am relatively new to CVXPY and any help would be appreciated!
Thanks!

[bstellato]

Haven't run the code but it looks like _x_mat parameter is not set. Did you forget to set its value?

[ShreyasFadnavis]

Thank you @bstellato ! Can you also point me to some example/ tutorial that solves some QP problem in a similar manner? I am unable to find some using OSQP...

[bstellato]

All the cvxpy problems that can be cast as QPs are solved by default with OSQP. For additional ones, you can check out the osqp docs.

[ShreyasFadnavis]

The same problem (mentioned above) was formulated and was working in CVXOPT as:

def _lstsq_initial(self, z):
        fodf_sh = csd._solve_cholesky(self._P, z)
        s = np.dot(self._reg, fodf_sh)
        init = {'x': cvx.matrix(fodf_sh),
                's': cvx.matrix(s.clip(1e-10))}
        return init

def __init__(self, X, reg):
        self._P = P = np.dot(X.T, X)
        self._X = X

        # No super res for now.
        assert _rank(P) == P.shape[0]

        self._reg = reg
        # self._P_init = np.dot(X[:, :N].T, X[:, :N])

        # Make cvxopt matrix types for later re-use.
        self._P_mat = cvx.matrix(P)
        self._reg_mat = cvx.matrix(-reg)
        self._h_mat = cvx.matrix(0., (reg.shape[0], 1))

def __call__(self, signal):
        z = np.dot(self._X.T, signal)
        init = self._lstsq_initial(z)

        z_mat = cvx.matrix(-z)
        qp = cvx.solvers.qp
        r = qp(self._P_mat, z_mat, self._reg_mat, self._h_mat, initvals=init)
        fodf_sh = r['x']
        fodf_sh = np.array(fodf_sh)[:, 0]
        return fodf_sh

I intend to just port this code to CVXPY.. Just facing a hard time in understanding how to!

[ShreyasFadnavis]

Thank you @bstellato ! Can you also point me to some example/ tutorial that solves some QP problem in a similar manner? I am unable to find some using OSQP...

I want self._x_mat to be my optimization variable. But when I set it up as:
self._x_mat = cvx.Variable(P.shape[0], 1)
It gives me a dcp error. As in:

objMin = cvx.Problem(cvx.Minimize(cvx.quad_form(self._x_mat, self._P_mat)))
objMin.is_dcp()

returns False. Am I doing something wrong in setting up the problem? Because in CVXOPT I did not have to explicitly set up the optimization variable and the interface was a little simpler to understand.

Any help would be super useful!
Thanks!

[ShreyasFadnavis]

@bstellato also, how can I set initvals in CVXPY as in CVXOPT? Is there an equivalent function to do so?

[SteveDiamond]

You cannot set initvals in CVXPY. It shouldn't matter too much for a QP, I would think.

[SteveDiamond]

The only way you could get objMin.is_dcp() to be False is if self._P_mat is not PSD, assuming everything has the correct dimensions.

[ShreyasFadnavis]

The only way you could get objMin.is_dcp() to be False is if self._P_mat is not PSD, assuming everything has the correct dimensions.

Hi Steven,

Thank you for your response! I think I have corrected this, by specifying the values in setting up the problem as follows:
objMin = cvx.Problem(cvx.Minimize(0.5 * cvx.quad_form(self._x_mat, self._P_mat.value) + z_mat.value.T * self._x_mat)), constraints)

Does this seem correct to you?

On doing the above, objMin.is_dcp() is returning True!

[ShreyasFadnavis]

You cannot set initvals in CVXPY. It shouldn't matter too much for a QP, I would think.

Thank you! I actually need this for another open-source project: DIPY (Diffusion Imaging in Python). The model needs to start the QP from a Cholesky Decomposition's initvals generated by another algorithm (Constrained Spherical Deconvolution).

I read that I could set the Variable.value to my primal initial point. Is there a way that I can make use of this to set the initvals as 'x' and 's' like in CVXOPT: QP ?

Thanks again :)

[SteveDiamond]

Unfortunately cvxpy does not yet support setting initial values. You can add it as a requested feature, though it's probably already in the TODOs.