GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
An extension of Newton-type algorithms for nonlinear process control
Automatica (Journal of IFAC)
Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
SIAM Journal on Optimization
A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control
SIAM Journal on Control and Optimization
Differential variational inequalities
Mathematical Programming: Series A and B
An algorithm for the fast solution of symmetric linear complementarity problems
Numerische Mathematik
An iterative approach for cone complementarity problems for nonsmooth dynamics
Computational Optimization and Applications
On the solution of complementarity problems arising in American options pricing
Optimization Methods & Software - Advances in Shape and Topology Optimization: Theory, Numerics and New Applications Areas
Barrier function based model predictive control
Automatica (Journal of IFAC)
A continuation/GMRES method for fast computation of nonlinear receding horizon control
Automatica (Journal of IFAC)
Convergence analysis of a parallel newton scheme for dynamic power grid simulations
Proceedings of the first international workshop on High performance computing, networking and analytics for the power grid
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We establish results for the problem of tracking a time-dependent manifold arising in real-time optimization by casting this as a parametric generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a single linear complementarity problem (LCP) at each time step. We derive sufficient conditions guaranteeing that the tracking error remains bounded to second order with the size of the time step even if the LCP is solved only approximately. We use these results to derive a fast, augmented Lagrangian tracking algorithm and demonstrate the developments through a numerical case study.