- CARMA OANT SEMINAR
- Speaker: Assoc Prof Regina Burachik, University of South Australia
- Title: Interior Epigraph Directions Method for Nonsmooth and Nonconvex Optimization via Generalized Augmented Lagrangian Duality
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Access Grid Venue: UniSA
- Time and Date: 2:00 pm, Tue, 26th Nov 2013
- Note earlier starting time.
We propose and study a new method, called the Interior Epigraph Directions (IED)
method, for solving constrained nonsmooth and nonconvex optimization. The IED
method considers the dual problem induced by a generalized augmented Lagrangian
duality scheme, and obtains the primal solution by generating a sequence of
iterates in the interior of the dual epigraph. First, a deflected subgradient
(DSG) direction is used to generate a linear approximation to the dual
problem. Second, this linear approximation is solved using a Newton-like step.
This Newton-like step is inspired by the Nonsmooth Feasible Directions Algorithm
(NFDA), recently proposed by Freire and co-workers for solving unconstrained,
nonsmooth convex problems. We have modified the NFDA so that it takes advantage
of the special structure of the epigraph of the dual function. We prove that all
the accumulation points of the primal sequence generated by the IED method are
solutions of the original problem. We carry out numerical experiments by using
test problems from the literature. In particular, we study several instances of
the Kissing Number Problem, previously solved by various approaches such as an
augmented penalty method, the DSG method, as well as the popular differentiable
solvers ALBOX (a predecessor of ALGENCAN), Ipopt and LANCELOT. Our experiments
show that the quality of the solutions obtained by the IED method is comparable
with (and sometimes favourable over) those obtained by the other solvers mentioned.
Joint work with Wilhelm P. Freire and C. Yalcin Kaya.
- [Permanent link]