The First-order And Second-order Necessary Conditions For Sparsity Constrained Optimization

As important properties in the theory of optimization,directional metric sub-regularity and mixed regularity/subregulaxity have vital effect on the stability of optimized feasibility and the analysis of optimal conditions.In this paper,we obtain the first-order and second-order sufficient conditions of directional metric subregulaxity and mixed regularity/subregulaxity of the set-valued mapping by the knowledge in variational analysis,further,we obtain the first-order and second-order necessary conditions for sparsity optimization problems,at the same time,we show the method and the result of calculation.