Graduate Students Seminar

Speaker 1: Emoke Galambos

Title

Preconditioning in Unconstrained Optimization Problems

Abstract

The L-BFGS method is a well-known Quasi-Newton method, which is widely used in large-scale, unconstrained optimization problems. In our numerical experiments we investigate the effects of preconditioning on the convergence of the L-BFGS method. Our goal is to test the algorithm on different variants of a popular benchmark function with a known global minimum. The test function is dominantly convex, with some perturbations. We explore some of the numerical instability issues caused by the ill-conditioning and the non-convexity of the objective functions. We also introduce a new algorithm that combines the preconditioned L-BFGS algorithm with a swarm optimization algorithm and complements the optimization problem with a randomized global search.

Speaker 2: John Eustaquio

Title

Statistical Inference in a Spatial-Temporal Stochastic Frontier Model

Abstract

The stochastic frontier model with heterogeneous technical efficiency explained by exogenous variables is augmented with a spatial-temporal component, a generalization relaxing the panel independence assumption in a panel data. The estimation procedure takes advantage of additivity in the model, computational advantages over simultaneous maximum likelihood estimation of parameters is exhibited. Estimates of the technical efficiency estimates are comparable to existing models estimated with maximum likelihood methods. The spatial-temporal component can improve estimates of technical efficiency in a production frontier that is usually biased downwards. We present a nonparametric test to verify model assumptions that facilitates estimation of parameters. Simulation studies indicate that the procedure is correctly-sized and powerful in a reasonably wide range of scenarios.