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Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…
Algorithms for computing fractional solutions to the quickest transshipment problem have been significantly improved since Hoppe and Tardos first solved the problem in strongly polynomial time. For integral solutions, runtime improvements…
The efficiency of any metaheuristic algorithm largely depends on the way of balancing local intensive exploitation and global diverse exploration. Studies show that bat algorithm can provide a good balance between these two key components…
This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…
Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method to produce solutions that are immunized against uncertainty. The main focus in robust…
The \Problem{knapsack} problem is a fundamental problem in combinatorial optimization. It has been studied extensively from theoretical as well as practical perspectives as it is one of the most well-known NP-hard problems. The goal is to…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
Reliable global optimization is dedicated to finding a global minimum in the presence of rounding errors. The only approaches for achieving a numerical proof of global optimality are interval branch and bound methods that interleave…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers respecting a given order of retrieval. While the problem is known…
Countless applications cast their computational core in terms of dense linear algebra operations. These operations can usually be implemented by combining the routines offered by standard linear algebra libraries such as BLAS and LAPACK,…
This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the…
In this paper, the scheduling problems of landing and takeoff aircraft on a same runway and on dual runways are addressed. In contrast to the approaches based on mixed-integer optimization models in existing works, our approach focuses on…
In this paper, we propose a practical online method for solving a class of distributionally robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
The standard oracle model for matroid algorithms assumes that each independence query can be answered in constant time, regardless of the size of the queried set. While this abstraction has underpinned much of the theoretical progress in…
Advances in artificial intelligence (AI) and deep learning have raised concerns about its increasing energy consumption, while demand for deploying AI in mobile devices and machines at the edge is growing. Binary neural networks (BNNs) have…
This paper develops an algorithmic solution using Ising machines to solve large-scale higher-order binary optimization (HOBO) problems with inequality constraints for resource optimization in wireless communications systems. Quadratic…
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…
Markov chain methods are remarkably successful in computational physics, machine learning, and combinatorial optimization. The cost of such methods often reduces to the mixing time, i.e., the time required to reach the steady state of the…