Resolution of equations – An optimization problem.

I have the following two quantities denoted by $ LHS $ Y $ RHS $

    LHS = Abs[
   p1 (z12 - z21) + I p2 (z12 - z21) + p3 (z11 - z22) + q (z11 + z22)];
RHS = Sqrt[Abs[z11]^ 2 + Abs[z21]^ 2]+ Sqrt[Abs[z12]^ 2 + Abs[z22]^ 2];

Here, $ zij $ ($ i, j = $ 1.2) are complex numbers. I need to find the values ​​of $ p1, p2, p3 $ Y $ q $, such that $ LHS> RHS $, subject to the condition that $ | q | + | vec {p} | le 1 $, where $ vec {p} = (p1, p2, p3) $.

This is my first question about Mathe-SE, sorry if you find the problem trivial or inappropriate in the description.