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)
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
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 .
for    do
 Update by flipping , the th bit of
if    then
  replace with
If , then is feasible