In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL-style calculus, using a composition of symbolical and numerical methods. To deal with the nonlinear components in case of conflicts we use numerically constructed restricted linearisations. This approach covers a large number of computable non-linear real functions such as polynomials, rational or trigonometrical functions and beyond. A prototypical implementation has been evaluated on several non-linear SMT-LIB examples and the results have been compared with state-of-the-art SMT solvers.
is a CDCL-style calculus for solving non-linear constraints over the real numbers involving polynomials and transcendental functions. In this paper we investigate properties of the calculus and show that it is a $$\delta $$
δ
-complete decision procedure for bounded problems. We also propose an extension with local linearisations, which allow for more efficient treatment of non-linear constraints.
Application domains of Bayesian optimization include optimizing black-box functions or very complex functions. The functions we are interested in describe complex real-world systems applied in industrial settings. Even though they do have explicit representations, standard optimization techniques fail to provide validated solutions and correctness guarantees for them. In this paper we present a combination of Bayesian optimisation and SMT-based constraint solving to achieve safe and stable solutions with optimality guarantees.
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