Computing Essential Sets for Convex and Nonconvex Scenario Problems: Theory and Application

The scenario approach is a general data-driven algorithm to chance-constrained optimization. It seeks the optimal solution that feasible carefully chosen number of scenarios. A crucial step in compute cardinality essential sets, which smallest subset scenarios determine solution. This article addresses challenge efficiently identifying sets. For convex problems, we demonstrate sparsest dual problem could pinpoint set. nonconvex show two simple algorithms return set when nondegenerate. Finally, illustrate theoretical results and computational on security-constrained unit commitment (SCUC) power systems. In particular, case studies SCUC are performed IEEE 118-bus system. Numerical suggest be an attractive practical system applications.