Unbounded objective function (mosek)

[Cyan Zhou]

I was using Mosek with YALMIP to solve a linear processing problem. The problem was successfully solved without objective function (only with constraints), while showed "unbounded objective function (mosek)" when adding the objective function. What is the reason for this error?

[Johan Löfberg]

https://yalmip.github.io/debuggingunbounded/

[Cyan Zhou]

Hi, I have carefully looked up my objective function, while I don't know why it is still unbounded. 

The problem I want to optimize is 

\min_{y} \sum_{(i,p)\in R} \lambda_{(i,p)} \sum_{k=1}^{|p|-1} w_{p_{k+1},p{k}} max\{-1, -\sum_{k'=1}^k y_{p_{k'},i} \}

s.t. y_{v,f} \in [0,1]

      \sum_{i \in C} y_{v,f} ==C_v, \forall v

      y_{v,f} = 1, \forall v \in S_f

Then, I use an auxiliary variable t_{p_k,i} to replace the max function in the objective function, and add two constraints shown as"

t_{p_k,i} >= -1

t_{p_k,i} >= -\sum_{k'=1}^k y_{p_{k'},i}

Then, the problem is to minimize the function in terms of variable y and variable t.

Is there anything resulting in the unboundness of the objective function?