Related papers: Learning efficient and provably convergent splitti…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by…
Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…
Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…
The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
Partitioning large machine learning models across distributed accelerator systems is a complex process, requiring a series of interdependent decisions that are further complicated by internal sharding ambiguities. Consequently, existing…
In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first…
In this paper, a non-uniform time-stepping convex-splitting numerical algorithm for solving the widely used time-fractional Cahn-Hilliard equation is introduced. The proposed numerical scheme employs the $L1^+$ formula for discretizing the…
The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…
We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows…
Linear systems with a tensor product structure arise naturally when considering the discretization of Laplace type differential equations or, more generally, multidimensional operators with separable coefficients. In this work, we focus on…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
We propose a splitting Hamiltonian Monte Carlo (SHMC) algorithm, which can be computationally efficient when combined with the random mini-batch strategy. By splitting the potential energy into numerically nonstiff and stiff parts, one…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…