Variational Analysis of Composite Models with Applications to Continuous Optimization

The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance which for numerous theoretical, algorithmic, applied issues operations research difficult overstate. underlying theme our systematical replacement conventional metric regularity related requirements by much weaker subregulatity ones that lead us significantly stronger completely new results first-order second-order optimization. In this way, we develop extended calculus rules generalized differential constructions while paying main attention theory rather large class fully subamenable compositions. Applications include deriving enhanced no-gap optimality conditions constrained models, complete characterizations uniqueness Lagrange multipliers, strong subregularity Karush-Kuhn-Tucker systems parametric optimization, so on.