Related papers: Adaptive strategies for solving parameterized syst…
We consider positive solutions to parametrized systems of generalized polynomial equations (with real exponents and positive parameters). By a fundamental result obtained in parallel work, polynomial systems are determined by geometric…
First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…
The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and…
This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…
The stationary points (SPs) of a potential energy landscape play a crucial role in understanding many of the physical or chemical properties of a given system. Unless they are found analytically, there is, however, no efficient method to…
We consider systems of strict multivariate polynomial inequalities over the reals. All polynomial coefficients are parameters ranging over the reals, where for each coefficient we prescribe its sign. We are interested in the existence of…
Given a C^1 path of systems of homogeneous polynomial equations f_t, t in [a,b] and an approximation x_a to a zero zeta_a of the initial system f_a, we show how to adaptively choose the step size for a Newton based homotopy method so that…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
Given a sensor network, TDOA self-calibration aims at simultaneously estimating the positions of receivers and transmitters, and transmitters time offsets. This can be formulated as a system of polynomial equations. Due to the elevated…
This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…
We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's flat degeneration to a toric variety. When Anderson's…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new…
We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring…