LMIs in Control/pages/LMI for convex minimization problem

The System
Let $$ A(x) $$ and $$ B(x) $$ are matrix functions of appropriate dimensions.

Moreove, the matrix functions $$ A(x) $$ and $$ B(x) $$ are linear in vector $$ x $$ where $$ x $$ is an $$m \times 1$$ vector.

The Data
A convex function $$ f(x) $$ is given and $$ x $$ is the vector of decision variables.

The Optimization Problem
The optimization problem is to minimize the convex function $$ f(x) $$ such that a contraint between two convex functions are satisfied for the decision variables.

The LMI: LMI for convex minimization problem
$$ \begin{align} &\text{min} \; \quad f(x)&\\ &A(x) < B(x) \end{align} $$

Implementation
A link to Matlab codes for this problem in the Github repository: