joint work with Dimitris Bertsimas, Jean Pauphilet
This talk provides a framework for deriving tractable non-linear reformulations of semi-continuous optimization problems. By imposing ridge or big-M penalty terms, we invoke strong duality to reformulate semi-continuous problems as tractable mixed-integer convex optimization problems. We also study the reformulation's continuous relaxation, provide a sufficient condition for tightness, and propose a randomized rounding scheme which provides high-quality warm-starts. Finally, we present promising computational results for facility location, network design and unit commitment problems.
joint work with Marta Betcke, Simon Arridge, Felix Lucka, Nam Huynh, Ben Cox, Edward Zhang, Paul Beard
In photoacoustic tomography, the acoustic propagation time across the specimen is the ultimate limit on sequential sampling frequency. In this talk, we first consider the photoacoustic reconstruction problem from compressed/subsampled measurements by utilizing sparsity in the Curvelet frame. Then we introduce the dynamic photoacoustic reconstruction from sub-sampled/compressed dynamic data using Curvelet sparsity in the photoacoustic image domain. Additionally, spatio-temporal regularization via optical flow constraint is applied.
joint work with Stephane Chretien, Andrew Thompson
We study the problem of super-resolution using TV norm minimisation, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. A practical approach is to solve the dual problem. In this talk, we study the stability of solutions with respect to the solutions to the dual problem. In particular, we establish a relationship between perturbations in the dual variable and the primal variables around the optimiser. This is achieved by applying a quantitative version of the implicit function theorem in a non-trivial way.