How to use cvx when it has auxiliary variable

Nonconvex
1

image
image686×606 126 KB

i am trying to solve this problem by cvx which is said to be a SOC constrained
problem .

variable t;
variable W1(2,2) complex;
variable V(2,2) complex;
A=trace(H1*W1)+trace(K1*V);
B=trace(Ke*V)-t*trace(Ke*W1)/(t-1);

But i don’t know how to express B.When it comes to ‘t*’ or something relative to t,it fails.And when i turn t into a specific number,it works.
how to fix this?all other variables is already known.

2

The first constraint would be an Second Order Cone constraint if t were input data. It is a non-convex constraint when t is an optimization (decision) variable. In the image,t should be listed as an optimization variable, because otherwise, maximizing it would not make sense (or it would just be a feasibility problem).

The problem is non-convex as written. So it either needs to be solved as a non-convex problem (you can try using YALMIP), or perhaps it is meant as part of an iterative scheme by which t is iterated or gridded, in which case maybe it is intended only as a feasibility problem, in which case including an objective of max t contributes to confusion.

Perhaps you need to study the paper or book you found this in more carefully.