Convex Optimization
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A Particle Swarm Optimization (PSO) algorithm is examined to solve the inverse problem in structural health monitoring. The damage detection problem is formulated as a PSO problem to find a damaged stiffness matrix that satisfies the structure's eigenequation and satisfying the necessary symmetry, sparsity, positive definiteness, and damage localization constraints. Finally, the PSO technique is compared to the Alternating Projection method in estimating damage using a simulated cantilever beam model.