Related papers: Block-Structured Integer and Linear Programming in…

Tight and efficient neural network bounding is crucial to the scaling of neural network verification systems. Many efficient bounding algorithms have been presented recently, but they are often too loose to verify more challenging…

In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node…

We consider 4-block $n$-fold integer programming, which can be written as $\max\{w\cdot x: H x=b, l\le x\le u, x\in \mathbb{Z}^{N} \}$ where the constraint matrix $H$ is composed of small submatrices $A,B,C,D$ such that the first row of $H$…

Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…

This paper proposes an algorithmic framework for various reconfiguration problems using zero-suppressed binary decision diagrams (ZDDs), a data structure for families of sets. In general, a reconfiguration problem checks if there is a…

We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…

Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…

Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

Computing the exact optimal experimental design has been a longstanding challenge in various scientific fields. This problem, when formulated using a specific information function, becomes a mixed-integer nonlinear programming (MINLP)…

The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…

The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…

We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…

This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…

We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…