# Primal-Dual Interior Methods for Nonlinear Optimization

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.

**Time:
**
Fri 2018-12-07 11.00 - 12.00

**Lecturer: **
Philip E. Gill, Department of Mathematics, University of California, San Diego

**Location: **
F11