Computable bounds on parametric solutions of convex problems
Mathematical Programming: Series A and B
Introduction to algorithms
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
On parametric semidefinite programming
HPOPT '96 Proceedings of the Stieltjes workshop on High performance optimization techniques
Journal of Optimization Theory and Applications
Convex Optimization
Delaunay partitions in Rn applied to non-convex programs and vertex/facet enumeration problems
Computers and Operations Research
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Brief An algorithm for multi-parametric quadratic programming and explicit MPC solutions
Automatica (Journal of IFAC)
Approximate explicit receding horizon control of constrained nonlinear systems
Automatica (Journal of IFAC)
Set Membership approximation theory for fast implementation of Model Predictive Control laws
Automatica (Journal of IFAC)
Multiobjective model predictive control
Automatica (Journal of IFAC)
Brief paper: On feasible sets for MPC and their approximations
Automatica (Journal of IFAC)
Explicit output-feedback nonlinear predictive control based on black-box models
Engineering Applications of Artificial Intelligence
On the global solution of multi-parametric mixed integer linear programming problems
Journal of Global Optimization
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For multiparametric convex nonlinear programming problems we propose a recursive algorithm for approximating, within a given suboptimality tolerance, the value function and an optimizer as functions of the parameters. The approximate solution is expressed as a piecewise affine function over a simplicial partition of a subset of the feasible parameters, and it is organized over a tree structure for efficiency of evaluation. Adaptations of the algorithm to deal with multiparametric semidefinite programming and multiparametric geometric programming are provided and exemplified. The approach is relevant for real-time implementation of several optimization-based feedback control strategies.