8 papers · 1 filter
A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimization
Chenyi Li, Zhijian Lai, Dong An +2
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for inte…
A Grover-compatible manifold optimization algorithm for quantum search
Zhijian Lai, Dong An, Jiang Hu +1
Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle an…
The Augmented Lagrangian Methods: Overview and Recent Advances
Kangkang Deng, Rui Wang, Zhenyuan Zhu +2
Large-scale constrained optimization is pivotal in modern scientific, engineering, and industrial computation, often involving complex systems with numerous variables and constrain…
SSNCVX: A primal-dual semismooth Newton method for convex composite optimization problem
Zhanwang Deng, Tao Wei, Jirui Ma +1
In this paper, we propose a uniform semismooth Newton-based algorithmic framework called SSNCVX for solving a broad class of convex composite optimization problems. By exploiting t…
Extended parameter shift rules with minimal derivative variance for parameterized quantum circuits
Zhijian Lai, Jiang Hu, Dong An +1
Parameter shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evalu…
Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity
Jiayuan Wu, Zhanwang Deng, Jiang Hu +2
We consider decentralized optimization over a compact Riemannian submanifold in a network of agents, where each agent holds a smooth, nonconvex local objective defined by its p…
LMask: Learn to Solve Constrained Routing Problems with Lazy Masking
Tianyou Li, Haijun Zou, Jiayuan Wu +1
Routing problems are canonical combinatorial optimization tasks with wide-ranging applications in logistics, transportation, and supply chain management. However, solving these pro…
An efficient primal dual semismooth Newton method for semidefinite programming
Zhanwang Deng, Jiang Hu, Kangkang Deng +1
In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semi…