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 | . |
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