Approximate multiparametric convex programming

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.