Computational Mathematics and Scientific Computing Seminar
Primal-Dual Interior Methods for Nonlinear Optimization
Speaker: Philip Gill, UCSD
Location: Warren Weaver Hall 1302
Date: Feb. 1, 2019, 10 a.m.
Regularization and stabilization are vital tools for resolving the numerical and theoretical difficulties associated with ill-posed or degenerate optimization problems. Broadly speaking, regularization involves perturbing the underlying linear equations so that they are always nonsingular. Stabilized methods are designed to provide a sequence of iterates with fast local convergence even when the gradients of the constraints satisfied at a solution are linearly dependent.
We discuss the crucial role of regularization and stabilization in the formulation and analysis of modern interior methods for nonlinear optimization. In particular, we establish the close relationship between regularization and stabilization, and propose a new interior method based on formulating an associated "simpler" optimization subproblem defined in terms of both primal and dual variables.