Related papers: Landscape of solutions in constraint satisfaction …
We introduce the framework of the left-hand side restricted promise constraint satisfaction problem, which includes problems like approximating clique number of a graph. We study the parameterized complexity of problems in this class and…
Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist,…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In this paper we provide an extended formulation for the class of constraint satisfaction problems and prove that its size is polynomial for instances whose constraint graph has bounded treewidth. This implies new upper bounds on extension…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
We investigate an algebraic problem related to the determination of the fundamental group of a class of spaces of configurations on surfaces. The configuration spaces are spaces of points grouped into colors. Whether two points are allowed…
Spectral methods include a family of algorithms related to the eigenvectors of certain data-generated matrices. In this work, we are interested in studying the geometric landscape of the eigendecomposition problem in various spectral…
The quantified constraint satisfaction problem (QCSP) is the problem of deciding, given a structure and a first-order prenex sentence whose quantifier-free part is the conjunction of atoms, whether or not the sentence holds on the…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…