multi-objective optimization

[Hamide Zebardast]

Hi,

Hope everything goes well,

I have solved multi-objective optimization problem on Complex circle manifold. The problem is attached. I have set the parameter " w = 1 " in the cost function  for the first. Now I want to optimize the problem subject to " w > 0 ". How should I solve the problem with this additional constraint? 

I will be so grateful if you help me. 

Best Regards,

Hamideh