Strong metric subregularity of the optimality mapping and second-order sufficient optimality conditions in extremal problems with constraints

This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization.It presents sufficient conditions for SMSR of the optimality mapping associated with a set of necessary optimality conditions in three types of constrained optimization problems: mathematical programming, calculus of variations, and optimal control.The conditions are based on second-order sufficient optimality conditions in the corresponding optimization problems and guarantee small changes in the optimal solution and Lagrange multipliers for small changes in the data.