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Journal of Optimization

Journal of Optimization / 2015 / Article / Alg 3

Research Article

Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities

Algorithm 3

Original-original (OO) constraint consensus algorithm.
INPUT: an initial point , a feasibility distance tolerance , a movement tolerance , maximum number of iterations and
Phase 1: as in the OD constraint Consensus Algorithm
Phase 2: (uses original basic consensus method directions)
Set
Set
While   and is infeasible do
 Set for all
 for every constraint   do
  if constraint is violated then
  
   Calculate feasibility vector
   for every variable in th constraint do
   ,
 for every variable in th constraint: do
  if    then
   
  else
   
Determine the LMI crossing points , with , on the consensus ray , and let denote
the constraint of the crossing point .
If there are no crossing points (i.e. ), set .
Set .
Set
Set
Set
for    do
 Update by flipping , the th bit of
 if    then
  replace with
  Set
Set
If , then is feasible
.