Papers › Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized...
Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized Clique Tree Conversion
Richard Y. Zhang, Javad Lavaei
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Clique tree conversion solves large-scale semidefinite programs by splitting an n×n matrix variable into up to n smaller matrix variables, each representing a principal submatrix of up to ω×ω. Its fundamental weakness is the need to introduce overlap constraints that enforce agreement between different matrix variables, because these can result in dense coupling. In this paper, we show that by dualizing the clique tree conversion, the coupling due to the overlap constraints is guaranteed to be sparse over dense blocks, with a block sparsity pattern that coincides with the adjacency matrix of a tree. We consider two classes of semidefinite programs with favorable sparsity patterns that encompass the MAXCUT and MAX k-CUT relaxations, the Lovasz Theta problem, and the AC optimal power flow relaxation. Assuming that ω≪n, we prove that the per-iteration cost of an interior-point method is linear O(n) time and memory, so an ϵ-accurate and ϵ-feasible iterate is obtained after O(√(n)log(1/ϵ)) iterations in near-linear O(n^(1.5)log(1/ϵ)) time. We confirm our theoretical insights with numerical results on semidefinite programs as large as n=13659. (Supporting code at https://github.com/ryz-codes/dual_ctc )
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections