# Examples

The gallery consists of standalone [Marimo](https://marimo.io/) notebooks from `examples/gallery`.
Each link opens an executed, non-interactive HTML snapshot containing the notebook code and outputs.
Published snapshots use $\epsilon_{\mathrm{target}}=10^{-5}$ to balance numerical validation and export time;
live sessions can request tighter continuation targets.

## Modeling primers

- {example}`Analytic quadratic <analytic_quadratic>`
  compares epsilon-relaxed solutions with a closed-form lower response.
- {example}`Optimistic linear program <optimistic_lp>`
  shows how the upper problem selects among tied lower optimizers.
- {example}`Parameter-dependent SOCP <parameter_dependent_socp>`
  derives a geometric response and inspects parameter-dependent canonical data.

- {example}`Best-of local optima <best_of_local_optima>`
  compares a deterministic local solve with several complete randomized runs.

## Applications

- {example}`Ridge hyperparameter selection <ridge_hyperparameter>`
  selects a training penalty using validation loss.
- {example}`Demand-response pricing <demand_response_pricing>`
  designs a time-of-use price while anticipating flexible energy use.
- {example}`Renewable-capacity planning <renewable_capacity_planning>`
  trades capacity investment against lower-level electricity dispatch.
- {example}`Traffic tolling <traffic_tolling>`
  selects tolls while anticipating a congestion equilibrium.
- {example}`Stackelberg port security <stackelberg_port_security>`
  allocates limited patrol coverage against a best-responding attacker.
- {example}`Planar truss sizing <planar_truss_sizing>`
  allocates member areas while anticipating elastic equilibrium.
- {example}`DC motor MPC tuning <dc_motor_mpc_tuning>`
  learns control-cost weights while anticipating a constrained MPC response.

## Advanced examples

Advanced examples are available as source notebooks in the repository. They are
checked statically and executed during release validation, but are not published
with the gallery.

- [Ridge-polishing decision](https://github.com/dxogrp/blvpy/blob/main/examples/advanced/ridge_polishing.py)
  retrains a validation-selected ridge model at its fixed penalty, then lets
  the user choose between lower-level feasibility and a better relaxed
  validation objective.
- [Low-carbon blend polishing](https://github.com/dxogrp/blvpy/blob/main/examples/advanced/low_carbon_blend_polishing.py)
  designs material rebates for a constrained producer, rejects a coarse
  polished response, tightens continuation, and explicitly adopts the
  candidate that passes a quantitative deployment gate.
- [Clean-equipment rebates](https://github.com/dxogrp/blvpy/blob/main/examples/advanced/clean_equipment_rebate.py)
  uses a three-dimensional power cone to design a rebate while anticipating
  a producer's clean and fossil input choices under Cobb--Douglas production.
- [Carbon-tax abatement](https://github.com/dxogrp/blvpy/blob/main/examples/advanced/carbon_tax_abatement.py)
  sets a carbon tax while anticipating sector-level abatement with
  exponential costs represented by exponential cones.

Browse all [repository examples](https://github.com/dxogrp/blvpy/tree/main/examples).

For live interaction, install and open the complete example workspace from a repository checkout:

```shell
make marimo
```