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Gradient flows are a powerful tool for optimizing functionals in general metric spaces, including the space of probabilities endowed with the Wasserstein metric. A typical approach to solving this optimization problem relies on its…

We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…

This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a…

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…

Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…

Network models provide an efficient way to represent many real life problems mathematically. In the last few decades, the field of network optimization has witnessed an upsurge of interest among researchers and practitioners. The network…

The motivation for this work stems from the problem of scheduling requests for flow at supply points along an automated network of open-water channels. The off-take flows are rigid-profile inputs to the system dynamics. In particular, the…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

In this technical report, a new formulation for embedding a neural network into an optimization model is described. This formulation does not require binary variables to properly compute the output of the neural network for specific types…

We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…

This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…

Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or…

Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…

The distinctive architectural features of normalizing flows (NFs), notably bijectivity and tractable Jacobians, make them well-suited for generative modeling. Invertible neural networks (INNs) build on these principles to address supervised…

Structured output prediction problems (e.g., sequential tagging, hierarchical multi-class classification) often involve constraints over the output label space. These constraints interact with the learned models to filter infeasible…

In this paper, we investigate the constraint typology of mixed-integer linear programming MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning,…

Transmission system operators face a variety of discrete operational decisions, such as switching of branches and/or devices. Incorporating these decisions into optimal power flow (OPF) results in mixed-integer non-linear programming…

The minimum k-partition problem is a challenging combinatorial problem with a diverse set of applications ranging from telecommunications to sports scheduling. It generalizes the max-cut problem and has been extensively studied since the…

The strengthening of linear relaxations and bounds of mixed integer linear programs has been an active research topic for decades. Enumeration-based methods for integer programming like linear programming-based branch-and-bound exploit…

We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…