For convex multiparametric 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. The case of multiparametric semidefinite programming is examined and exemplified on a test example. The approach opens up the application of explicit receding horizon techniques to several robust model predictive control schemes based on convex optimization, such as linear matrix inequalities.

Approximate multiparametric convex programming

A. BEMPORAD;
2003-01-01

Abstract

For convex multiparametric 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. The case of multiparametric semidefinite programming is examined and exemplified on a test example. The approach opens up the application of explicit receding horizon techniques to several robust model predictive control schemes based on convex optimization, such as linear matrix inequalities.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/2813
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