Solvers¶

This page is a sparse map of the solver families exposed by PYDGENS. It is not yet a full theory guide.

Linear-Quadratic Games¶

The LQ path solves finite-horizon linear-quadratic dynamic games for feedback Nash strategies.

Used by:

• tug_o_war.py
• satellite_lady_bandit_guard.py

Theory notes:

• TODO: summarize finite-horizon coupled Riccati/backward-recursion structure.
• TODO: document sign conventions and frontend-to-IR quadratic scaling.
• References: Dynamic Noncooperative Game Theory, Feedback LQ Nash Derivation.

Iterative Linear-Quadratic Games¶

The iLQ path repeatedly builds local linear-quadratic approximations of a nonlinear game and solves those approximations for local feedback Nash updates.

Used by:

• unicycle.py
• multi_car_intersection.py

Theory notes:

• TODO: summarize local game approximation, feedback update, and line-search behavior.
• TODO: clarify convergence diagnostics and failure modes.
• References: iLQGames, Smooth Game Theory.

Augmented-Lagrangian Games¶

The AL path targets constrained nonlinear games with local open-loop trajectories. This solver path is currently beta/pre-release.

Used by:

• constrained_integrators.py

Theory notes:

• TODO: document the augmented-Lagrangian state, multiplier updates, and regularization strategy.
• TODO: explain which constraints are currently supported by the frontend.
• Reference: ALGAMES.