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Journal of Optimization
/
2015
/
Article
/
Alg 1
Research Article
Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities
Algorithm 1
Original-DBmax (OD) constraint consensus algorithm.
INPUT: An initial point
, a feasibility distance tolerance
, a movement tolerance
, maximum number of iterations
and
Phase 1:
Do the original basic constraint consensus method, Algorithm 1 in [
9
], using the parameters
,
and
and starting from
to get a near-feasible point.
Let
be the last iterate of Phase 1. (Remark:
is the starting point of Phase 2.)
Phase 2:
(uses DBmax consensus method directions given in [
9
])
Set
Set
While
and
is infeasible
do
Set
,
,
,
,
for each variable
for
every constraint
do
if
constraint
is violated
then
Calculate feasibility vector
for
every variable
in
th constraint
do
if
then
if
then
else if
then
if
then
for
every variable
:
do
if
then
else 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
.