GEAR: A GPU-Accelerated Global Solver for Bounded Continuous Nonlinear Programs via Linear Bound Propagation

Duo Zhou, Hesun Chen, Xiangru Zhong, Grani A. Hanasusanto, Huan Zhang

We present a novel GPU-accelerated global solver for constrained nonlinear programming (NLP) inspired by the efficient linear bound propagation framework in neural network (NN) verification. Existing work on NN verification, a problem that can be cast as feasibility detection for a nonlinear objective, demonstrated orders-of-magnitude speedups with the linear bound propagation-based framework when compared to traditional solvers. Extending this paradigm to global nonlinear programming requires addressing many challenges: a global constrained NLP solver must effectively exploit all, possibly unstructured, nonlinear constraints to improve the objective, whereas NN verification typically handles simple input box constraints over a well-structured NN and does not directly optimize an objective function. We address these challenges by fully exploiting the linear bounds produced by bound propagation: these linear bounds can be viewed as relaxations of nonlinear constraints and used to provide lower bounds, check infeasibility, and guide the search for a primal solution. In addition, we propose tighter linear relaxations for bilinear, quotient, and other commonly used nonlinear…