TL;DR
This paper establishes that every bounded sequence generated by Gi-PSADMM with the variance-reduced stochastic gradient estimator converges globally to a critical point in expectation and derives the convergence rate of Gi-PSADMM that depends on the KL exponent.
A hyperbolic-majorization preconditioned three-term nonlinear conjugate-gradient framework for nonconvex finite minimax optimization that yields a Dai--Liao-type conjugacy relation, enhanced sufficient descent, a smoothing-parameter-uniform Armijo lower bound, fixed-smoothing global first-order convergence and complexi...
In this paper, we propose a balanced augmented Lagrangian method based on accelerated stochastic ADMM (b-ASADMM) to efficiently solve structured separable nonconvex optimization problems subject to linear constraints. The objective function in this problem comprises potentially nonsmooth and smooth functions, where the...
A globally convergent regularized Newton method with positive definite regularization for solving nonsmooth optimization problems that replaces the identity matrix in traditional algorithms with a general positive-definite symmetric matrix to regularize the generalized Hessian.
It is shown that Fr\'echet or proximal stationarity can be characterized through asymptotic vanishing of the proposed measure along some convergent sequence and analogous asymptotic results for a smoothing-based variant of the measure are established.
Empirical results reveal that VR-DR remains highly effective for nonsmooth loss functions, significantly broadening its practical utility beyond its theoretical constraints.
Four groups of subspace methods for nonlinear monotone equations, with applications to large-scale machine learning problems, using Jacobian-free subspace directions of conjugate-gradient type combined with either fixed step sizes or variable step sizes generated by the projected method of Solodov and Svaiter are intro...
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