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I have a sparse optimization problem of the form:

$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$

This includes also some constraints, so it is a non-purely quadratic problem here (I will have to use CVXPY to solve this)

$D$ is diagonal and $V$, $W$ are non-square matrices. I know that: $$Q = D^2 + V V^T - WW^T \succ 0$$

is positive definite. Ensuring convexity of the problem, but optimizing with dense matrix $Q$ is very slow.

Can we rewrite this problem so that it is accepted by a DCP solver like CVXPY, while keeping sparse structure of the problem ?

I have a sparse optimization problem of the form:

$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$

$D$ is diagonal and $V$, $W$ are non-square matrices. I know that: $$Q = D^2 + V V^T - WW^T \succ 0$$

is positive definite. Ensuring convexity of the problem, but optimizing with dense matrix $Q$ is very slow.

Can we rewrite this problem so that it is accepted by a DCP solver like CVXPY, while keeping sparse structure of the problem ?

PS: problem also includes some constraints, so is non-quadratic

I have a sparse optimization problem of the form:

$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$

$D$ is diagonal and $V$, $W$ are non-square matrices. I know that: $$Q = D^2 + V V^T - WW^T \succ 0$$

is positive definite. Ensuring convexity of the problem, but optimizing with dense matrix $Q$ is very slow.

Can we rewrite this problem so that it is accepted by a DCP solver like CVXPY, while keeping sparse structure of the problem ?

I have a sparse optimization problem of the form:

$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$

This includes also some constraints, so it is a non-purely quadratic problem here (I will have to use CVXPY to solve this)

$D$ is diagonal and $V$, $W$ are non-square matrices. I know that: $$Q = D^2 + V V^T - WW^T \succ 0$$

is positive definite. Ensuring convexity of the problem, but optimizing with dense matrix $Q$ is very slow.

Can we rewrite this problem so that it is accepted by a DCP solver like CVXPY, while keeping sparse structure of the problem ?

I have a sparse optimization problem of the form:

$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$

Subject to constraints.

$D$ is diagonal and $V$, $W$ are non-square matrices. I know that: $$Q = D^2 + V V^T - WW^T \succ 0$$

is positive definite. Ensuring convexity of the problem, but optimizing with dense matrix $Q$ is very slow.

Can we rewrite this problem so that it is accepted by a DCP solver like CVXPY, while keeping sparse structure of the problem ?

I have a sparse optimization problem of the form:

$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$

$D$ is diagonal and $V$, $W$ are non-square matrices. I know that: $$Q = D^2 + V V^T - WW^T \succ 0$$

is positive definite. Ensuring convexity of the problem, but optimizing with dense matrix $Q$ is very slow.

Can we rewrite this problem so that it is accepted by a DCP solver like CVXPY, while keeping sparse structure of the problem ?