Related papers: Delta-modular ILP Problems of Bounded Codimension,…
Integer linear programs (ILPs) are a widely applied framework for dealing with combinatorial problems that arise in practice. It is known, e.g., by the success of CPLEX, that preprocessing and simplification can greatly speed up the process…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at…
Solving convex Semi-Infinite Programming (SIP) problems is challenging when the separation problem, i.e., the problem of finding the most violated constraint, is computationally hard. We propose to tackle this difficulty by solving the…
Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this…
By using representation theory, we reduce the size of the set of possible values for the dimension of the convex hull of all feasible points polytope of an orthogonal array (OA) defining integer linear program (ILP). Our results address the…
Given a matrix $A$ and $k\geq 0$, we study the problem of finding the $k\times k$ submatrix of $A$ with the maximum determinant in absolute value. This problem is motivated by the question of computing the determinant-based lower bound of…
We design and analyze primal-dual, feasible interior-point algorithms (IPAs) employing full Newton steps to solve convex optimization problems in standard conic form. Unlike most nonsymmetric cone programming methods, the algorithms…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints…
DPLL and resolution are two popular methods for solving the problem of propositional satisfiability. Rather than algorithms, they are families of algorithms, as their behavior depend on some choices they face during execution: DPLL depends…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…
Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…
In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT…
In recent work, Darmon, Pozzi and Vonk explicitly construct a modular form whose spectral coefficients are $p$-adic logarithms of Gross-Stark units and Stark-Heegner points. Here we describe how this construction gives rise to a practical…
In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and…
To solve unmodeled optimization problems with hard constraints, this paper proposes a novel zeroth-order approach called Safe Zeroth-order Optimization using Linear Programs (SZO-LP). The SZO-LP method solves a linear program in each…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…
We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…