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Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…
By employing non-equispaced grid points near boundaries, boundary-optimized upwind finite-difference operators of orders up to nine are developed. The boundary closures are constructed within a diagonal-norm summation-by-parts (SBP)…
We propose a fundamental setup for the realization of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of the nonlinear Schroedinger equation with the self-attractive and repulsive cubic…
We investigate the construction and performance of summation-by-parts (SBP) operators, which offer a powerful framework for the systematic development of structure-preserving numerical discretizations of partial differential equations.…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
A bipartite bilinear program (BBP) is a quadratically constrained quadratic optimization problem where the variables can be partitioned into two sets such that fixing the variables in any one of the sets results in a linear program. We…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language. This richer formalism comes at the price of higher computational…
In this paper we begin by discussing the simple bilevel programming problem (SBP) and its extension the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their…