Multistart algorithm for identifying all optima of nonconvex stochastic functions

Journal Article · 06 May 2024 · Optimization Letters

DOI: https://doi.org/10.1007/s11590-024-02114-z · OSTI ID:2476909

Jaiswal, Prateek  ^[1]; Larson, Jeffrey ^[2]

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1. Texas A & M Univ., College Station, TX (United States)
2. Argonne National Laboratory (ANL), Argonne, IL (United States)

Here, we propose a multistart algorithm to identify all local minima of a constrained, nonconvex stochastic optimization problem. The algorithm uniformly samples points in the domain and then starts a local stochastic optimization run from any point that is the "probabilistically best" point in its neighborhood. Under certain conditions, our algorithm is shown to asymptotically identify all local optima with high probability; this holds even though our algorithm is shown to almost surely start only finitely many local stochastic optimization runs. We demonstrate the performance of an implementation of our algorithm on nonconvex stochastic optimization problems, including identifying optimal variational parameters for the quantum approximate optimization algorithm.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 2476909
• Journal Information: Optimization Letters, Journal Name: Optimization Letters Journal Issue: 6 Vol. 18; ISSN 1862-4472
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English