相关论文: A Computational Status Update for Exact Rational M…

We introduce a software package called HIFIR for preconditioning sparse, unsymmetric, ill-conditioned, and potentially singular systems. HIFIR computes a hybrid incomplete factorization, which combines multilevel incomplete LU factorization…

Schedulability is a fundamental problem in real-time scheduling, but it has to be approximated due to the intrinsic computational hardness. As the most popular algorithm for deciding schedulability on multiprocess platforms, the speedup…

In this paper, we propose a Pre-trained Mixed Integer Optimization framework (PreMIO) that accelerates online mixed integer program (MIP) solving with offline datasets and machine learning models. Our method is based on a data-driven…

Mixed Integer programs (MIPs) are typically solved by the Branch-and-Bound algorithm. Recently, Learning to imitate fast approximations of the expert strong branching heuristic has gained attention due to its success in reducing the running…

Prompt optimization has become crucial for enhancing the performance of large language models (LLMs) across a broad range of tasks. Although many research papers demonstrate its effectiveness, practical adoption is hindered because existing…

This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…

We present a two-level branch-and-bound (BB) algorithm to compute the optimal gripper pose that maximizes a grasp metric in a restricted search space. Our method can take the gripper's kinematics feasibility into consideration to ensure…

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this…

A recently proposed exact algorithm for the maximum independent set problem is analyzed. The typical running time is improved exponentially in some parameter regions compared to simple binary search. The algorithm also overcomes the core…

In this paper we derive an efficient method for computing the indices associated with an asymptotically optimal upper confidence bound algorithm (MDP-UCB) of Burnetas and Katehakis (1997) that only requires solving a system of two…

Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…

The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is…

Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong…

Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics,…

Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with…

We provide the global optimization community with new optimality proofs for six deceptive benchmark functions (five bound-constrained functions and one nonlinearly constrained problem). These highly multimodal nonlinear test problems are…

This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…

An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of 5 and low-order additive terms. $M$ optimally distributes resources between the…

We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a…

Group Relative Policy Optimization (GRPO) has become a standard approach for training mathematical reasoning models; however, its reliance on multiple completions per prompt makes training computationally expensive. Although recent work has…