Related papers: Fix-and-Propagate Heuristics Using Low-Precision F…

We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key…

This paper discusses the fixed-hub single allocation problem (FHSAP). In this problem, a network consists of hub nodes and terminal nodes. Hubs are fixed and fully connected; each terminal node is connected to a single hub which routes all…

We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…

Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite…

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…

Given a flow network, the Minimum Flow Decomposition (MFD) problem is finding the smallest possible set of weighted paths whose superposition equals the flow. It is a classical, strongly NP-hard problem that is proven to be useful in RNA…

We study the convergence behaviors of primal-dual hybrid gradient (PDHG) for solving linear programming (LP). PDHG is the base algorithm of a new general-purpose first-order method LP solver, PDLP, which aims to scale up LP by taking…

When the quality of naive prompts is carefully optimized by human experts, the task performance of large language models (LLMs) can be significantly improved. However, expert-based prompt optimizations are expensive. Herein, some works have…

Recently, hybrid metaheuristics have become a trend in operations research. A successful example combines the Greedy Randomized Adaptive Search Procedures (GRASP) and data mining techniques, where frequent patterns found in high-quality…

Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor…

Large language models (LLMs) are computationally intensive. The computation workload and the memory footprint grow quadratically with the dimension (layer width). Most of LLMs' parameters come from the linear layers of the transformer…

The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…

We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is…

In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…

Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…

The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions are much more expensive than low-fidelity ones. To reduce the…

With the increasing demand for computing capability given limited resource and power budgets, it is crucial to deploy applications to customized accelerators like FPGAs. However, FPGA programming is non-trivial. Although existing high-level…

The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…

Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a linear program (LP)…