Branch-and-bound performance estimation programming: a unified methodology for constructing optimal optimization methods
Author(s)
Das Gupta, Shuvomoy
Van Parys, Bart P. G.
Ryu, Ernest K.
Date Issued
June 7, 2023
Journal
Mathematical Programming
Publisher
Springer Science and Business Media LLC
Citation
Das Gupta, S., Van Parys, B.P.G. & Ryu, E.K. Branch-and-bound performance estimation programming: a unified methodology for constructing optimal optimization methods. Math. Program. 204, 567–639 (2024).
Version
Author's final manuscript
Abstract
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.
Subjects
General Mathematics
Software
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10107-023-01973-1
