(136f) Unipopt: Univariate Projection-Based Optimization without Derivatives
We have extensively tested the UNIPOPT framework using many test problems from literature. For instance, we applied it to solve 393 bound-constrained black-box problems comprising of 232 nonconvex smooth problems and 161 convex nonsmooth problems taken from Rios and Sahinidis . Its performance has been compared to other DFO solvers such as BOBYQA, ORBIT, SNOBFIT and IMFIL. For the test suite of nonconvex smooth problems, UNIPOPT finds solutions within 1% of the global minima for 10â65% more problems compared to these solvers. For convex nonsmooth problems, UNIPOPT can solve 20-30% more problems to 1% global optimality. In terms of convergence, we show that UNIPOPT converges to local minima when certain conditions are satisfied. The UNIPOPT framework is further extended to handle constrained black-box problems. Specifically, we will present the performance of the algorithm against other DFO solvers that can handle constraints for 92 numerical problems taken from GlobalLib. UNIPOPT finds solutions within 1% of the global optimality for 20-52% more problems than those solved by the other solvers.
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