The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is known to be NP-hard. In this paper, we present a neighborhood search heuristic called LK-INSERT which uses a Lin-Kernighan neighborhood … Read more
The contributions of the first half of this thesis are on the computational and algebraic aspects of convexity in polynomial optimization. We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves … Read more
Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets. Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in … Read more
In this paper we consider robust models of surge capacity plans to be deployed in the event of a flu pandemic. In particular, we focus on managing critical staff levels at organizations that must remain operational during such an event. We develop efficient procedures for managing emergency resources so as to minimize the impact of … Read more
We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. for a family of nonnegative matrices). In case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and … Read more
Two nonlinear Kalman smoothers are proposed using the Student’s t distribution. The first, which we call the T-Robust smoother, finds the maximum a posteriori (MAP) solution for Gaussian process noise and Student’s t observation noise. It is extremely robust against outliers, outperforming the recently proposed L1-Laplace smoother in extreme situations with data containing 20% or … Read more
It is well-known that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for a quadratic Lyapunov function. Since homogeneous vector fields of even degree can never be AS, the next interesting degree to consider is equal to three. In this … Read more
The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present … Read more
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of … Read more
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of … Read more