Derives linear sample complexity for PDHG parameters and polynomial sample complexity for full PDLP hyperparameters using data-driven algorithm design.
Restarted Halpern PDHG for linear programming
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CHAP's cross-platform portfolio finds feasible solutions for 47 of 50 MIP benchmark instances in five minutes, beating Gurobi (44) and cuOpt (43) by coordinating GPU tabu search with CPU fix-and-propagate and feasibility pump via a shared pool.
Derives accessible O(κΦ ln(κΦ ||w*||/ε)) iteration bound for rPDHG on unique-optima LPs, with computable Φ, two-stage performance, and equivalence to stability and sharpness.
DSPDHG extends PDHG and SPDHG with doubly stochastic block updates and proves O(1/K) ergodic convergence for the expected restricted primal-dual gap plus linear convergence for a restarted variant under quadratic growth.
A geometric analysis shows PDHG on LP produces a spiral dynamic with orthogonal rotation and forward components, which is used to design a new non-simplex crossover algorithm for vertex solutions.
lpviz is a web-based interactive visualization tool for linear programming that enables direct graphical editing of problems and comparison of multiple solver algorithms in 2D and 3D.
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