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Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
Graph Generation is a recently introduced enhanced Column Generation algorithm for solving expanded Linear Programming relaxations of mixed integer linear programs without weakening the expanded relaxations which characterize these methods.…
Column generation (CG) is a powerful technique for solving optimization problems that involve a large number of variables or columns. This technique begins by solving a smaller problem with a subset of columns and gradually generates…
We consider a fashion discounter that supplies any of its many branches with an integral multiple of lots whose size assortment structure stems from a set of many applicable lot-types. We design a column generation algorithm for the optimal…
Bilevel programming can be used to formulate many problems in the field of power systems, such as strategic bidding. However, common reformulations of bilevel problems to mixed-integer linear programs make solving such problems hard, which…
Robust iterative methods for solving large sparse systems of linear algebraic equations often suffer from the problem of optimizing the corresponding tuning parameters. To improve the performance of the problem of interest, specific…
This paper develops column partition based distributed schemes for a class of large-scale convex sparse optimization problems, e.g., basis pursuit (BP), LASSO, basis pursuit denosing (BPDN), and their extensions, e.g., fused LASSO. We are…
Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant…
Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…
The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
The multi-commodity flow (MCF) problem is a fundamental topic in network flow and combinatorial optimization, with broad applications in transportation, communication, and logistics, etc. Nowadays, the rapid expansion of allocation systems…
The team formation and routing problem is a challenging optimization problem with several real-world applications in fields such as airport, healthcare, and maintenance operations. To solve this problem, exact solution methods based on…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
Periodic timetabling for public transportation networks is typically modelled as a Periodic Event Scheduling Problem (PESP). Solving instances of the benchmark library PESPlib to optimality continues to pose a challenge. As a further…
We introduce a simple, accurate, and extremely efficient method for numerically solving the multi-marginal optimal transport (MMOT) problems arising in density functional theory. The method relies on (i) the sparsity of optimal plans [for…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…
The column-and-constraint generation (CCG) method was introduced by \citet{Zeng2013} for solving two-stage adaptive optimization. We found that the CCG method is quite scalable, but sometimes, and in some applications often, produces…