Applied Mathematics Colloquium

Title:

Inexact Sequential Quadratic Programming

Abstract:

Sequential Quadratic Programming (SQP) methods represent a powerful class of algorithms for minimizing continuous functions subject to continuous constraints.  They are particularly effective on small- to medium-scale problems, and on large-scale problems when a good initial estimate of the solution is available.  When a good initial estimate of a solution is not available for large-scale problems, interior-point methods are typically the algorithms of choice since their cost per iteration is the solution of a linear system of equations. In contrast, traditional SQP methods require the solution of a quadratic program during each iteration, which is the main hurdle that prevents traditional SQP methods from scaling to large-scale problems, in general.  In this talk I present recent work on inexact SQP that aims at overcoming the difficulties with scalability.  Specifically, we have developed conditions that allow for the calculation of inexact solutions to all subproblems that arise in a penalty-SQP framework. Preliminary numerical results will be provided.