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We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Linearization Technique into standard SDP relaxations while…

Optimization and Control · Mathematics 2026-02-13 Aida Khajavirad

Traditional post-training quantization (PTQ) is considered an effective approach to reduce model size and accelerate inference of large-scale language models (LLMs). However, existing low-rank PTQ methods require costly fine-tuning to…

Machine Learning · Computer Science 2026-01-12 Hongyaoxing Gul , Lijuan Hu , Shuzi Niu , Fangfang Liu

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we…

In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…

Optimization and Control · Mathematics 2023-05-18 Yingzhe Xu , Cheng Lu , Zhibin Deng , Ya-Feng Liu

The distributed recursion (DR) algorithm is an effective method for solving the pooling problem that arises in many applications. It is based on the well-known P-formulation of the pooling problem, which involves the flow and quality…

Optimization and Control · Mathematics 2024-11-15 Wei-Yang Zhang , Feng-Lian Dong , Zhi-Wei Wei , Yan-Ru Wang , Ze-Jin Xu , Wei-Kun Chen , Yu-Hong Dai

A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…

Systems and Control · Electrical Eng. & Systems 2026-03-30 Leilei Cui , Richard D. Braatz

GRPO-style reinforcement learning (RL)-based LLM fine-tuning algorithms have recently gained popularity. Relying on heuristic trust-region approximations, however, they can lead to brittle optimization behavior, as global importance-ratio…

Machine Learning · Computer Science 2026-02-09 Doyeon Lee , Eunyi Lyou , Hyunsoo Cho , Sookyung Kim , Joonseok Lee , Jaemoo Choi

Pruning is a common technique to reduce the compute and storage requirements of Neural Networks. While conventional approaches typically retrain the model to recover pruning-induced performance degradation, state-of-the-art Large Language…

Machine Learning · Computer Science 2025-10-16 Christophe Roux , Max Zimmer , Alexandre d'Aspremont , Sebastian Pokutta

Reinforcement learning (RL) problems can be challenging without well-shaped rewards. Prior work on provably efficient RL methods generally proposes to address this issue with dedicated exploration strategies. However, another way to tackle…

Machine Learning · Computer Science 2023-06-21 Qiyang Li , Yuexiang Zhai , Yi Ma , Sergey Levine

Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…

Optimization and Control · Mathematics 2026-03-31 Muge Dedeoglu , Buket Ozen , Burak Kocuk

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

Quantum Physics · Physics 2018-08-20 Patrick Rebentrost , Maria Schuld , Leonard Wossnig , Francesco Petruccione , Seth Lloyd

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that…

Quantum Physics · Physics 2025-02-21 Austin Yubo He , Zi-Wen Liu

A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and…

Numerical Analysis · Computer Science 2016-05-18 Mohammad M. Mansour

Large language models (LLMs) are omnipresent, however their practical deployment is challenging due to their ever increasing computational and memory demands. Quantization is one of the most effective ways to make them more compute and…

Machine Learning · Computer Science 2024-09-04 Yelysei Bondarenko , Riccardo Del Chiaro , Markus Nagel

This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical…

Machine Learning · Computer Science 2024-11-12 Jahid Hasan

Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…

Quantum Physics · Physics 2021-04-07 Keren Li , Pan Gao , Shijie Wei , Jiancun Gao , Guilu Long

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the…

Optimization and Control · Mathematics 2013-03-22 Cordian Riener , Thorsten Theobald , Lina Jansson Andrén , Jean B. Lasserre

In this paper, we propose new linearly convergent second-order methods for minimizing convex quartic polynomials. This framework is applied for designing optimization schemes, which can solve general convex problems satisfying a new…

Optimization and Control · Mathematics 2022-01-14 Yurii Nesterov

Declarative spatial reasoning denotes the ability to (declaratively) specify and solve real-world problems related to geometric and qualitative spatial representation and reasoning within standard knowledge representation and reasoning (KR)…

Artificial Intelligence · Computer Science 2015-06-17 Carl Schultz , Mehul Bhatt

Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…

Optimization and Control · Mathematics 2017-09-27 Aurélien Ouattara , Anil Aswani