### Daniel Robinson (University of Oxford and Rutherford Appleton Laboratory)

#### Recent advances in second-derivative sequential quadratic programming methods

*Wednesday 10 February 2010 at 15.30, JCMB 6206*

##### Abstract

The first part of this talk is an introduction to sequential quadratic
programming (SQP) methods. Specifically, I will i) describe the basic
formulation of SQP methods; ii) discuss why SQP methods form a class of very
efficient algorithms for solving nonlinear nonconvex optimization problems;
and iii) address the main algorithmic difficulties that arise when constructing
SQP methods that utilize exact second-derivative information.

The second part of the talk will be focus on recent advances in
second-derivative SQP methods. Most of the time will be devoted to
describing S2QP: a Fortran 90 implementation of an SQP algorithm that is
globally and superlinearly convergent, incorporates second-derivative
information efficiently, and utilizes subproblems that are either convex
(may be solved efficiently) or need not be solved globally; S2QP may be
viewed as an improvement to the Sl_{1}QP method by Fletcher since he
requires the global minimizer of indefinite QP subproblems to prove global
convergence, which is known to be NP-hard. I will also present limited
numerical results from the CUTEr test set, which indicate that S2QP is at
least capable of solving (efficiently) some large problems consisting of
10,000-100,000 variables/constraints.

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