Related papers: On the feasibility of generalized inverse linear p…
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…
We consider the problem of deciding, given a sequence of regions, if there is a choice of points, one for each region, such that the induced polyline is simple or weakly simple, meaning that it can touch but not cross itself. Specifically,…
A multiset $\Lambda=\{\lambda_1,\ldots,\lambda_n\}$ of complex numbers is said to be realizable whenever there exists a nonnegative matrix of order $n$ with spectrum $\Lambda$. One of the broadest criterion that guarantees realizability is…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
We introduce the concept of inverse feasibility for linear forward models as a tool to enhance OTA FL algorithms. Inverse feasibility is defined as an upper bound on the condition number of the forward operator as a function of its…
We explore the inverse of integer programs (IPs) by studying the inverse of their Gomory corner relaxations (GCRs). We show that solving a set of inverse GCR problems always yields an upper bound on the optimal value of the inverse IP that…
Algorithms are ways of mapping problems to solutions. An algorithm is invertible precisely when this mapping is injective, such that the initial problem can be uniquely inferred from its solution. While invertible algorithms can be…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
The workflow satisfiability problem is concerned with determining whether it is possible to find an allocation of authorized users to the steps in a workflow in such a way that all constraints are satisfied. The problem is NP-hard in…
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…
The Hospital Residents setting models important problems like school choice, assignment of undergraduate students to degree programs, among many others. In this setting, fixed quotas are associated with the programs that limit the number of…
We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…