Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones

Algorithm 3

Backtracking line search technique.

INPUTS: set of 𝑞 constraints (1.1) or (3.1), a point 𝑥, the consensus vector 𝑡

Compute the binary word 𝑏 at 𝑥

count = 0

while  count<3  do

 𝛼=1+0.5^count

 𝑥temp=𝑥+𝛼∗𝑡

 Compute the binary word 𝑏comp at 𝑥temp

 if  (𝑏comp)≤sum(𝑏)  then

  𝑥=𝑥temp; Exit Function

 else

  count = count+1

if count = loop then

 𝑥=𝑥+𝑡