Invited Session Wed.1.H 0107

Wednesday, 10:30 - 12:00 h, Room: H 0107

Cluster 16: Nonlinear programming [...]

Regularization techniques in optimization I


Chair: Jacek Gondzio



Wednesday, 10:30 - 10:55 h, Room: H 0107, Talk 1

Jacek Gondzio
Recent advances in the matrix-free interior point method


The matrix-free interior point method allows for solving
very large optimization problems without the need to have
them explicitly formulated. The method uses problem matrices
only as operators to deliver the results of matrix-vector
Recent advances including the new theoretical insights
and the new computational results will be presented.



Wednesday, 11:00 - 11:25 h, Room: H 0107, Talk 2

Paul Armand
A boundedness property of the Jacobian matrix arising in regularized interior-point methods

Coauthor: Joël Benoist


We present a uniform boundedness property of a sequence of inverses of Jacobian matrices that arises in regularized primal-dual interior-point methods in linear and nonlinear programming. We then show how this new result can be applied to the analysis of the global convergence properties of these methods. In particular, we will detail the convergence analysis of an interior point method to solve nonlinear optimization problems, with dynamic updates of the barrier parameter.



Wednesday, 11:30 - 11:55 h, Room: H 0107, Talk 3

Michael Saunders
QPBLUR: A regularized active-set method for sparse convex quadratic programming

Coauthor: Christopher Maes


QPBLUR is designed for large convex quadratic programs with many
degrees of freedom. (Such QPs have many variables but relatively few
active constraints at a solution, and cannot be solved efficiently by
null-space methods.) QPBLUR complements SQOPT as a solver for the
subproblems arising in the quasi-Newton SQP optimizer SNOPT.
QPBLUR uses a BCL algorithm (bound-constrained augmented Lagrangian)
to solve a given QP. For each BCL subproblem, an active-set method
solves a large KKT system at each iteration, using sparse LU factors
of an initial KKT matrix and block-LU updates for a series of
active-set changes. Primal and dual regularization ensures that the
KKT systems are always nonsingular, thus simplifying implementation
and permitting warm starts from any starting point and any active set.
There is no need to control the inertia of the KKT systems, and a
simple step-length procedure may be used without risk of cycling in
the presence of degeneracy.
We present the main features of QPBLUR and some numerical results from
the Fortran 95 implementation on a test set of large convex QPs and on
the QPs arising within SNOPT.


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