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 biased augmented multiplier signal, shifting the equilibria of the mean dynamics. For componentwise inequalities, we give a necessary and sufficient condition for preserving the Karush-Kuhn-Tucker (KKT) equilibria and construct a convex example with a locally exponentially stable equilibrium that violates complementarity. To address this bias, constraint values are estimated recursively before forming the augmented multiplier signal. For smooth convex conic problems, a joint energy analysis establishes boundedness of the primal, dual, and estimation states, vanishing estimation error, and almost sure convergence of the primal-dual iterates to a single KKT point under global regularity and bounded conditional second moments. The result allows nonunique solutions and multipliers while keeping the number of samples per iteration fixed. Numerical studies illustrate the predicted equilibrium bias and examine convergence with nonunique KKT points and nonlinear constraints.
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...
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
To address the issue that existing penalty weight update strategies in the augmented Lagrangian multiplier method are disconnected from the optimality conditions and remain relatively sensitive to initial parameters, this paper proposes a complementarity-gap-driven adaptive sequential convex programming algorithm. The...
Lei-Lei Wu, Cheng-Long Dong, Peng Wang et al.· Aerospace· 0 citations
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 un...
R. Andreani, G. Haeser, R. W. Prado et al.· 6 citations· ⚡3
This paper studies constrained optimization problems through the lens of feedback control. Building on the interpretation of Lagrange multipliers as feedback controllers, we propose the \emph{saddle-point PID (SPPID) dynamics}: a unified proportional--integral--derivative (PID) framework for continuous-time saddle-poin...
Veronica Centorrino, Rawan Hoteit, Efe C. Balta et al.· 0 citations
Adaptive AI agents can help make BIM data more machine-readable by navigating IFC models, interpreting inconsistent information, and mapping it to defined standards. In this blog, Alok Rawat shares findings from a real-world pilot in construction workflows. The post Adaptive AI Agents in Construction Workflows appeared first on GPT-Lab.
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