Optimization Days 2017
HEC Montréal, May 8-10, 2017
1st Canadian Healthcare Optimization Workshop (CHOW)
HEC Montréal, May 10-11, 2017
HEC Montréal, 8 — 11 May 2017
WB3 Méthodes d'optimisation / Optimization methods
May 10, 2017 10:30 AM – 12:10 PM
Chaired by Ryan Caverly
10:30 AM - 10:55 AM
Service systems with adjustable speed
We investigate a fluid model of a service system, in which customers are discharged at an adjustable speed, which influences the proportion of customers that require rework after a delay. We formulate the model as a delay-differential equation. We study the transient and steady-state behavior of the system occupancy in four different regimes and we obtain conditions under which speedup reduces average occupancy.
10:55 AM - 11:20 AM
Factorization-free methods for computed tomography
We study a tomographic reconstruction problem in cylindrical coordinates. A change of variables involving a Fourier matrix attempts to improve the conditioning of the Hessian but introduces linear inequality constraints. The scale and density of the problem call for factorization-free methods. We argue that projections into the feasible set can be computed efficiently by solving a bound-constrained least-squares problem with a fast linear operator. In this talk, we focus on a Barzilai-Borwein projected gradient method and a trust-region projected Newton method. We compare two solvers for the projection subproblem: a two-metric projection algorithm and a trust-region projected Newton method. The performance of several combinations is assessed using synthetic data on the reconstruction problem.
11:20 AM - 11:45 AM
Extremum-Seeking Guidance on SO(3) Using a Kalman Filter
Extremum-seeking guidance endeavours to drive the output of a system to the extremum of an unknown objective function. This paper proposes an extremum-seeking guidance algorithm for constrained subsets of SO(3). The algorithm is enabled by a novel constrained Kalman filter, and is demonstrated on a spacecraft attitude guidance problem.
11:45 AM - 12:10 PM
Controller Design for Regional Pole and Zero Placement using Linear Matrix Inequalities and the Modified Minimum Gain Lemma
This talk presents controller synthesis methods involving linear matrix inequalities that place closed-loop zeros in the open left-half complex plane. This prevents nonminimum phase closed-loop behaviour, often characterized by a response that initially moves in the opposite direction from a desired set point before asymptotically reaching the desired set point.