Access Type

Open Access Dissertation

Date of Award

January 2020

Degree Type


Degree Name




First Advisor

Boris Mordukhovich


The dissertation is devoted to the study of the first- and second-order variational analysis of the composite functions with applications to composite optimization. By considering a fairly general composite optimization problem, our analysis covers numerous classes of optimization problems such as constrained optimization; in particular, nonlinear programming, second-order cone programming and semidefinite programming(SDP). Beside constrained optimization problems our framework covers many important composite optimization problems such as the extended nonlinear programming and eigenvalue optimization problem. In first-order analysis we develop the exact first-order calculus via both subderivative and subdifferential. For the second-order part we develop calculus rules via second-order subderivative (which was a long standing open problem). Furthermore, we establish twice epi-differentiability of composite functions. Then we apply our results to composite optimization problem to obtain first- and second-order order optimality conditions under the weakest constraint qualification, the metric subregularity constraint qualification. Finally we apply our results to verify the super linear convergence in SQP methods for constrained optimization.