I would like to minimize the following objective function

$$ || H \circ A - (H \cdot I) \circ B ||_F^2 $$

w.r.t. $H$. Here, $H$, $I$, $A$, and $B$ are all square matrices of the same size. $\circ$ denotes convolution and $\cdot$ is matrix multiplication. $I$ is a flipped identity matrix (i.e., off-diagonal elements are 1 and others 0).

I would like to ask are there any common routines to solve a problem involving convolution? Also, is this problem convex?

Edit:

I first considered to apply FFT on both $H \circ A$ and $ (H \cdot I) \circ B$. This however still cannot eliminate all convolution operations from the objective.

I would like to minimize the following objective function

$$ \| H \ast A - (H \cdot I) \ast B \|_F^2 $$

w.r.t. $H$, where

• $H$, $I$, $A$, and $B$ are all square matrices of the same size ($I$ is a flipped identity matrix i.e., off-diagonal elements are 1 and others 0),
• $\ast$ denotes convolution and
• $\cdot$ is the matrix multiplication.

I would like to ask: are there any common routines to solve a problem involving convolution? Also, is this problem convex?

Edit:

I first considered to apply FFT on both $H \ast A$ and $ (H \cdot I) \ast B$. This however still cannot eliminate all convolution operations from the objective.

I would like to minimize the following objective function

$$ || H \circ A - (H \cdot I) \circ B ||_F^2 $$

w.r.t. $H$. Here, $H$, $I$, $A$, and $B$ are all square matrices of the same size. $\circ$ denotes convolution and $\cdot$ is matrix multiplication. $I$ is a flipped identity matrix (i.e., off-diagonal elements are 1 and others 0).

I would like to ask are there any common routines to solve a problem involving convolution? Also, is this problem convex?

I would like to minimize the following objective function

$$ || H \circ A - (H \cdot I) \circ B ||_F^2 $$

w.r.t. $H$. Here, $H$, $I$, $A$, and $B$ are all square matrices of the same size. $\circ$ denotes convolution and $\cdot$ is matrix multiplication. $I$ is a flipped identity matrix (i.e., off-diagonal elements are 1 and others 0).

I would like to ask are there any common routines to solve a problem involving convolution? Also, is this problem convex?

Edit:

I first considered to apply FFT on both $H \circ A$ and $ (H \cdot I) \circ B$. This however still cannot eliminate all convolution operations from the objective.