Optimization Modulo Non-linear Arithmetic via Incremental Linearization

Filippo Bigarella, Alessandro Cimatti, Alberto Griggio, Ahmed Irfan, Martin Jonás, Marco Roveri, Roberto Sebastiani, Patrick Trentin

Abstract: Incremental linearization is a conceptually simple, yet effective, technique that we have recently proposed for solving SMT problems on the theories of non-linear arithmetic over the reals and the integers. Optimization Modulo Theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions. In this paper, we show how incremental linearization can be extended to OMT in a simple way, producing an incomplete though effective OMT procedure. We describe the main ideas and algorithms, we provide an implementation within the OptiMathSAT OMT solver, and perform an empirical evaluation. The results support the effectiveness of the approach.