Hard-constrained signal feasibility problems

We consider the problem of synthesizing feasible signals in the presence of inconsistent convex constraints, some of which are hard in the sense that they must absolutely be satisfied. This problem is formalized as that of minimizing an objective function measuring the degree of unfeasibility with respect to the soft constraints over the intersection of the sets associated with the hard constraints. We first investigate the process of aggregating soft constraints in order to define relevant objectives and then address the question of solving the resulting convex programs. Finally, we provide numerical results to illustrate the benefits of our analysis.