5 papers · 1 filter
Sharp Initialization Guarantees for the Heavy-Ball Method
Kang Liu, Quanen Wu, Zhan Sun +3
The heavy-ball method can accelerate convergence near the minimizer, but it may also enter persistent oscillations on general strongly convex objectives. How should it be initializ…
Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints
Kang Liu, Mengxiao Chen, Siqi Xiong +1
This work studies the stability and convergence of augmented primal-dual dynamics when constraint values are estimated from samples. Unbiased constraint observations can produce a…
Residual-Controlled Douglas--Rachford Splitting for Differentiable Solver Layers
Kang Liu, Jianchen Hu
Differentiable solver layers embed constrained optimization into end-to-end learning systems, but fixed-depth unrolling must trade off solution quality, feasibility, and computatio…
Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making
Kang Liu, Jianchen Hu, Ziyu Qu +3
Stochastic constrained decision-making requires optimizing performance objectives while enforcing statistical requirements such as safety or fairness. However, standard primal--dua…
SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions
Kang Liu, Jianchen Hu, Wei Peng
Classical ReLU-based Input Convex Neural Networks (ICNNs) are equivalent to the optimal value functions of Linear Programming (LP). This intrinsic structural equivalence restricts…