2023-06-07
Branch-and-bound performance estimation programming: A unified methodology for constructing optimal optimization methods
Publication
Publication
Mathematical Programming Series B , Volume 204 p. 567- 639
We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal optimization method as a nonconvex but practically tractable quadratically constrained quadratic optimization problem and solves it to certifiable global optimality using a customized branch-and-bound algorithm. By directly confronting the nonconvexity, BnB-PEP offers significantly more flexibility and removes the many limitations of the prior methodologies. Our customized branch-and-bound algorithm, through exploiting specific problem structures, outperforms the latest off-the-shelf implementations by orders of magnitude, accelerating the solution time from hours to seconds and weeks to minutes. We apply BnB-PEP to several setups for which the prior methodologies do not apply and obtain methods with bounds that improve upon prior state-of-the-art results. Finally, we use the BnB-PEP methodology to find proofs with potential function structures, thereby systematically generating analytical convergence proofs.
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doi.org/10.1007/s10107-023-01973-1 | |
Mathematical Programming Series B | |
van Parys, B., Gupta, S. D., & Ryu, E. K. (2023). Branch-and-bound performance estimation programming: A unified methodology for constructing optimal optimization methods. Mathematical Programming Series B, 204, 567–639. doi:10.1007/s10107-023-01973-1 |