麻省理工学院（Massachusetts Institute of Technology），简称“麻省理工”（MIT），位于美国马萨诸塞州波士顿都市区剑桥市，主校区依查尔斯河而建，是一所世界著名私立研究型大学。麻省理工学院创立于1861年，早期侧重应用科学及工程学，在第二次世界大战后，麻省理工学院倚靠美国国防科技的研发需要而迅速崛起。在二战和冷战期间，麻省理工学院的研究人员对计算机、雷达以及惯性导航系统等科技发展作出了重要贡献。 麻省理工学院素以顶尖的工程与技术而著名，拥有麻省理工人工智能实验室（MIT CSAIL）、林肯实验室（MIT Lincoln Lab）和麻省理工学院媒体实验室（MIT Media Lab），其研究人员发明了万维网（www）、GNU系统、Emacs编辑器、RSA算法等等。 该校的计算机工程、电机工程等诸多工程学领域在2019-20年软科世界大学学科排名中位列世界前五，在2018-19年US News美国研究生院排名中位列工程学第一、计算机科学第一，与斯坦福大学、加州大学伯克利分校一同被称为工程技术界的学术领袖。截至2020年10月，麻省理工学院的校友、教职工及研究人员中，共产生了97位诺贝尔奖得主（世界第五）、8位菲尔兹奖得主（世界第七）以及26位图灵奖得主（世界第二）。麻省理工学院位列2021-22年度QS世界大学排名第一 、U.S. News世界大学排名第二 、莫斯科国际大学排名第二 、软科世界大学学术排名第四 、泰晤士高等教育世界大学排名第五 。同时列2020泰晤士高等教育世界大学声誉排名世界第二 。
We present a new algorithm for solving large-scale security-constrained optimal power flow in polar form (AC-SCOPF). The method builds on Nonlinearly Constrained augmented Lagrangian (NCL), an augmented Lagrangian method in which the subproblems are solved using an interior-point method. NCL has two key advantages for large-scale SCOPF. First, NCL handles difficult problems such as infeasible ones or models with complementarity constraints. Second, the augmented Lagrangian term naturally regularizes the Newton linear systems within the interior-point method, enabling solution of the Newton systems with a pivoting-free factorization that can be efficiently parallelized on GPUs. We assess the performance of our implementation, called MadNCL, on large-scale corrective AC-SCOPFs, with complementarity constraints modeling the corrective actions. Numerical results show that MadNCL can solve AC-SCOPF with 500 buses and 256 contingencies fully on the GPU in less than 3 minutes, whereas Knitro takes more than 3 hours to find an equivalent solution.
As GPU-accelerated mathematical programming techniques mature, there is growing interest in utilizing them to address the computational challenges of power system optimization. This paper introduces ExaModelsPower.jl, an open-source modeling library for creating GPU-compatible nonlinear AC optimal power flow models. Built on ExaModels.jl, ExaModelsPower.jl provides a high-level interface that automatically generates all necessary callback functions for GPU solvers. The library is designed for large-scale problem instances, which may include multiple time periods and security constraints. Using ExaModelsPower.jl, we benchmark GPU and CPU solvers on open-source test cases. Our results show that GPU solvers can deliver up to two orders of magnitude speedups compared to alternative tools on CPU for problems with more than 20,000 variables and a solution precision of up to 10−4, while performance for smaller instances or tighter tolerances may vary.
Reinforcement learning (RL) has shown great potential for designing voltage control policies, but their performance often degrades under changing system conditions such as topology reconfigurations and load variations. We introduce a topology-aware online policy optimization framework that leverages data-driven estimation of voltage-reactive power sensitivities to achieve efficient policy adaptation for medium-voltage radial distribution networks. Exploiting the sparsity of topology-switching events, where only a few lines change at a time, our method efficiently detects topology changes and identifies the affected lines and parameters, enabling fast and accurate sensitivity updates without recomputing the full sensitivity matrix. The estimated sensitivity is subsequently used for online policy optimization of a pre-trained neural-network-based RL controller. Simulations on both the IEEE 13-bus and SCE 56-bus systems demonstrate over 90% line identification accuracy, using only 15 data points. The proposed method also significantly improves voltage regulation performance compared with non-adaptive policies and adaptive policies that rely on regression-based online optimization methods for sensitivity estimation.
We prove a refinement of Jackson's theorem on the approximation of Lipschitz functions by trigonometric polynomials. Our result precisely characterizes the leading error term associated with Jackson's construction. We do the same for a related construction commonly used in the kernel polynomial method for spectral density estimation, which is slightly better than Jackson's construction in this respect.
Jaccard similarity is a natural measure for set-like objects such as binary vectors, with various applications including plagiarism detection and association rule mining. A fundamental optimization problem in this context is Jaccard Center-given a collection of sets over a universe, find a subset of the universe minimizing the maximum Jaccard distance to any of the sets. Bury and Schwiegelshohn [ICALP '17] gave a PTAS and ruled out an FPTAS. In this short note, we show that under the standard assumption FPT not equal W[1], Jaccard Center admits no EPTAS. Hence, the existing PTAS qualitatively cannot be strengthened.
