Nonsmooth Newton’s Method and Semidefinite Optimization
We introduce basic ideas of a nonsmooth Newton’s method and its application in solving semidefinite optimization (SDO) problems. In particular, the method can be used to solve both linear and nonlinear semidefinite complementarity problems. We also survey recent theoretical results in matrix functions and stability of SDO that are stemed from the research on the matrix form of the nonsmooth Newton’s method.
High Performance Computation for Engineered Systems (HPCES);
semismooth functions, semidefinite optimization, Newton’s method, complementarity problems, stability, variational inequality