Related papers: Revisiting Performance of BiCGStab Methods for Sol…
Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often…
Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods…
Synchronized dual-arm rearrangement is widely studied as a common scenario in industrial applications. It often faces scalability challenges due to the computational complexity of robotic arm rearrangement and the high-dimensional nature of…
Enhancing the efficiency of iterative computation on graphs has garnered considerable attention in both industry and academia. Nonetheless, the majority of efforts focus on expediting iterative computation by minimizing the running time per…
For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the…
This paper proposes improving the solve time of a bootstrap AMG designed previously by the authors. This is achieved by incorporating the information, set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single…
Benders decomposition (BD), along with its generalized version (GBD), is a widely used algorithm for solving large-scale mixed-integer optimization problems that arise in the operation of process systems. However, the off-the-shelf…
Early scheduling algorithms usually adjusted the clock cycle duration to the execution time of the slowest operation. This resulted in large slack times wasted in those cycles executing faster operations. To reduce the wasted times…
A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is…
ML(n)BiCGStab is a Krylov subspace method for the solution of large, sparse and non-symmetric linear systems. In theory, it is a method that lies between the well-known BiCGStab and GMRES/FOM. In fact, when n = 1, ML(1)BiCGStab is BiCGStab…
We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems…
We propose Mstab, a novel Krylov subspace recycling method for the iterative solution of sequences of linear systems with fixed system matrix and changing right-hand sides. This new method is a straight and simple generalization of IDRstab.…
A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order…
In this paper, we propose a bootstrap method applied to massive data processed distributedly in a large number of machines. This new method is computationally efficient in that we bootstrap on the master machine without over-resampling,…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…
Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we propose a parallel procedure for solving tridiagonal systems of equations with Toeplitz matrices. Taking the structure of the Toeplitz matrices, we may substantially…