Significance Many scientific and engineering fields, including optimization, machine learning, and quantum computing, use semidefinite programming (SDP) to tackle complex problems. Unfortunately, as these problems grow, they rapidly exceed the capabilities of conventional SDP solvers, creating a critical bottleneck. By...
Qiu-Shi Han, Zhen-Wei Lin, Han-Wen Liu et al.· Proceedings of the National...· 1 citation
Let $\Delta_u(d,n)$ be the maximum graph diameter of a pointed $d$-dimensional polyhedron with $n$ facets. Using a curved-path encoding of the iterated Kalai--Kleitman recurrence, we prove, uniformly over $n\geq d\geq 4$, \[ \Delta_u(d,n) \leq (n-d)^{\log_2 G_d},\qquad G_d = (4\ln 2+o(1))\frac{d}{(\ln d)^2}, \] where t...
This work shows empirically that solver-integrated reasoning, exact combinatorial algorithm, and heuristic search exhibit complementary strengths across different problem structures and scales, and introduces Strategy-Diverse Reinforcement Learning (SDRL), which trains LLMs as adaptive optimization meta-solvers.
Shi-Hao Zhang, Wei-Ting Liu, Si-Yu Shao et al.· 0 citations
PDHCG-CQP achieves state-of-the-art robustness among first-order solvers while scaling efficiently to 8 GPUs and instances with up to $4.4\times10^8$ stored primal coordinates.
Hongpei Li, Yicheng Huang, Hui-Kang Liu et al.· 3 citations
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