Lara Zebiane An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for cases when objective function and generalized gradient values might be subject to bounded uncontrollable errors. Similarly to state-of-the-art guarantees for noisy smooth optimization … Read more
Identifying active constraints from a point near an optimal solution is important both theoretically and practically in constrained continuous optimization, as it can help identify optimal Lagrange multipliers and essentially reduces an inequality-constrained problem to an equality-constrained one. Traditional active-set identification guarantees have been proved under assumptions of smoothness and constraint qualifications, and assume exact … Read more
NonOpt, a C++ software package for minimizing locally Lipschitz objective functions, is presented. The software is intended primarily for minimizing objective functions that are nonconvex and/or nonsmooth. The package has implementations of two main algorithmic strategies: a gradient-sampling and a proximal-bundle method. Each algorithmic strategy can employ quasi-Newton techniques for accelerating convergence in practice. The … Read more