**Reference:**

J. Xu,
T. van den Boom, and
B. De Schutter,
"Optimistic optimization for continuous nonconvex piecewise affine
functions," *Automatica*, Mar. 2021. Article 109476.

**Abstract:**

This paper considers global optimization of a continuous nonconvex
piecewise affine (PWA) function over a polytope. This type of
optimization problem often arises in the context of control of
continuous PWA systems. In literature, it has been shown that the
given problem can be formulated as a mixed integer linear programming
(MILP) problem, the worst-case complexity of which grows exponentially
with the number of polyhedral subregions in the domain of the PWA
function. In this paper, we propose a solution approach that is more
efficient for continuous PWA functions with a large number of
polyhedral subregions. The proposed approach is based on optimistic
optimization, which uses hierarchical partitioning of the feasible set
and which can guarantee bounds on the suboptimality of the returned
solution with respect to the global optimum given a prespecified
finite number of iterations. Since the function domain is a polytope
with arbitrary shape, we introduce a partitioning approach by
employing Delaunay triangulation and edgewise subdivision. Moreover,
we derive the analytic expressions for the core parameters required by
optimistic optimization for continuous PWA functions. The numerical
example shows that the resulting algorithm is faster than MILP solvers
for PWA functions with a large number of polyhedral subregions.

Online version of the paper

Corresponding technical report: pdf file (262 KB)

@article{Xuvan:15-030,

author={J. Xu and T. van den Boom and B. {D}e Schutter},

title={Optimistic optimization for continuous nonconvex piecewise affine functions},

journal={Automatica},

month=mar,

year={2021},

note={Article 109476},

doi={10.1016/j.automatica.2020.109476}

}

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