Invited Session Tue.1.H 0110

Tuesday, 10:30 - 12:00 h, Room: H 0110

Cluster 16: Nonlinear programming [...]

Nonlinear optimization IV


Chair: Frank E. Curtis and Daniel Robinson



Tuesday, 10:30 - 10:55 h, Room: H 0110, Talk 1

Jaroslav Fowkes
Global optimization of Lipschitz continuous functions

Coauthors: Coralia Cartis, Chris L. Farmer, Nicholas I.m. Gould


We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularization techniques to a radial-basis model of the objective over balls that form an overlapping covering of the feasibility domain. Numerical results for both serial and parallel implementations will be provided.



Tuesday, 11:00 - 11:25 h, Room: H 0110, Talk 2

Roger Fletcher
On trust regions and projections for an SLCP algorithm for NLP


The speaker has recently developed a first derivative trust region filter algorithm for NLP (SIOPT Darmstadt 2011) based on successive linear constraint programming (SLCP) (Robinson's method). Open source code is available through COIN-OR. Numerical evidence suggests that it is comparable in run time to the second derivative code filterSQP. An important feature of the code is the occasional use of projection steps to control feasibility violations, which can significantly improve the speed of (global) convergence on some highly nonlinear problems.
Discussions with other researchers have identified a possible area for improvement in that these projection steps take no account of the objective function value, in contrast say to second order correction (SOC) steps. The speaker has been investigating the possibility of replacing projection steps by additional LCP calculations. New insight is provided as to how a trust region might be designed to operate in an NLP context. Early indications are that significant gains in both speed and reliability may be possible, both in feasibility restoration and in finding local optimality. There are also indications for proving global convergence.



Tuesday, 11:30 - 11:55 h, Room: H 0110, Talk 3

Jennifer Erway
Quasi-Newton methods for solving the trust-region subproblem


In this talk, we consider quasi-Newton trust-region methods for large-scale unconstrained optimization. A new trust-region subproblem solver is proposed that is able to take advantage of the special structure of quasi-Newton approximations to Hessians. The method relies on a sequence evolving, low-dimensional subspaces. Numerical results compare the proposed method with other popular quasi-Newton trust-region methods in various trust-region settings.


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