LSDO Lab
Methods

Provably convergent distributed optimization architectures

Context
Multidisciplinary design problems can be divided into smaller optimizations when memory limits or disciplinary boundaries prevent a monolithic solution.
Gap
Equivalent distributed formulations need not yield convergent algorithms, and constraints spanning several disciplines complicate subproblem coordination.
Research goal
Establish convergent distributed algorithms that enforce global constraints while keeping model evaluations within their assigned subproblems.

Selected studies

References
Block-coordinate descentGlobal constraint coordination

Recovering system solutions from smaller subproblems

Block coordinate descent solves disciplinary subproblems sequentially without a system-level optimizer, with convergence to a stationary point proved for the unconstrained formulation under stated assumptions. Control co-design and aerostructural tests recover monolithic solutions; distributed warm starts improve convergence reliability in the aerostructural tests. Peak memory stays constant as cart-pole trajectory copies are added, while the monolithic formulation's memory grows.

Primary paper

Nicholas C. Orndorff, John T. Hwang. A Distributed Method for Solving Large-Scale Multidisciplinary Optimization Problems. AIAA AVIATION FORUM AND ASCEND 2025, 2025.

DOIPDF
A cart-pole co-design trajectory is paired with the convergence history of distributed coordinate descent toward the monolithic objective value.
Distributed block coordinate descent reduces the cart-pole co-design objective toward the monolithic solution through sequential subproblem updates. Fig. 4, Orndorff and Hwang, 2025 [1]
Peak memory use and solution time compare monolithic and distributed formulations as the number of cart-pole trajectories increases.
As the number of cart-pole trajectory copies increases, the distributed formulation limits peak memory per subproblem while requiring additional solution time. Fig. 6, Orndorff and Hwang, 2025 [1]

Satisfying constraints across disciplinary boundaries

An augmented Lagrangian enforces global and consensus constraints without driving penalty coefficients to infinity. Copies of shared variables and intermediate quantities let each subproblem evaluate only its own models. An aerostructural test converges, while the more expensive blended-wing-body run demonstrates decreasing solution error without reaching tight convergence.

Primary paper

Nicholas C. Orndorff, Christopher Lupp, John T. Hwang. A Distributed Algorithm for Large-Scale Multidisciplinary Design Optimization With Global Constraints. AIAA AVIATION 2026 Forum, 2026. Distribution Statement A: Approved for public release; distribution is unlimited. PA# AFRL-2026-2045

DOIPDF
N-squared diagram of the blended-wing-body optimization problem shows the disciplinary models and variables coordinated by the distributed algorithm.
The BWB N-squared diagram identifies the coupled disciplinary quantities and global constraints coordinated by the distributed formulation. Fig. 13, Orndorff et al., 2026 [2]
BWB solution error and absolute design-variable values are plotted across inner-loop iterations of the distributed algorithm.
BWB solution error decreases as the design variables stabilize; the reported run stops before tight convergence. Fig. 14, Orndorff et al., 2026 [2]

References

  1. Nicholas C. Orndorff, John T. Hwang. A Distributed Method for Solving Large-Scale Multidisciplinary Optimization Problems. AIAA AVIATION FORUM AND ASCEND 2025, 2025.
    DOIPDF
  2. Nicholas C. Orndorff, Christopher Lupp, John T. Hwang. A Distributed Algorithm for Large-Scale Multidisciplinary Design Optimization With Global Constraints. AIAA AVIATION 2026 Forum, 2026. Distribution Statement A: Approved for public release; distribution is unlimited. PA# AFRL-2026-2045
    DOIPDF
  3. Sebastiaan P. van Schie, Marius L. Ruh, Andrew H. Fletcher, Michael Warner, Mark Sperry, Luca Scotzniovsky, Nicholas C. Orndorff, Ru Xiang, Jiayao Yan, Han Zhao, Joshua Krokowski, Jiun-Shyan Chen, Darshan Sarojini, Hyunjune Gill, Seongkyu Lee, Andrew C. Tagg, Ryan Anderson, Eric Green, Cibin Joseph, Andrew Ning, Zeyu Cheng, Zhi Cao, Chunting Mi, Alexandre T. Guibert, Ashley Cronk, Alicia A. Kim, Shirley Meng, Christopher Silva, John T. Hwang. Large-Scale Distributed Multidisciplinary Design Optimization of the NASA Lift-Plus-Cruise Air Taxi Concept. AIAA SCITECH 2025 Forum, 2025.
    DOIPDF

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