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 | . |
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