It is proved that the Error Bound Constraint Qualification is the weakest constraint qualification that guarantees boundedness of the computed multiplier sequences generated by the augmented Lagrangian method, and the feasibility of accumulation points of primal sequences generated by the augmented Lagrangian method under a Polyak-Łojasiewicz inequality for the quadratic infeasibility measure.
We consider convex optimization with nonlinear inequality constraints and develop a primal-dual multiplier framework that is consistent in continuous and discrete time. We first propose continuous-time dynamics with Nesterov-type vanishing damping $\alpha/t$, together with compatible extrapolations of the dual variable...
It is shown that strict complementarity, together with a quadratic facial-violation property of the associated complementary faces, implies uniform quadratic growth of both the primal and dual augmented Lagrangians near a strictly complementary solution, and the local equivalence of three regularity conditions is prove...
It is shown that any first-order method guaranteeing a bound on the primal objective gap f(x_N)-f(x_\star) assuming only a bound on $\|x_0-x_\star\|$ actually has a stronger guarantee on an explicit, computable primal-dual gap at the same rate.
In this paper, we study a Tikhonov-regularized mixed-order primal--dual dynamical system with implicit Hessian damping for linearly constrained convex optimization problems in finite-dimensional Euclidean spaces, where the primal equation is second order and incorporates the viscous damping term \(\delta\sqrt{\varepsil...
This work proposes a nonlinear-residual linearized augmented Lagrangian method (NR-LALM) that replaces this subproblem by a regularized Gauss-Newton-type step while retaining the classical multiplier update based on the nonlinear constraint residual.
Ben-Qi Liu, Kangkang Deng, Zichen Wang et al.· 0 citations
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...
