Solver families

pylcm exposes one broad solver and a family of structural specializations.

The map¶

The table is not a ranking. Each row solves a different declared problem class.

EGM-family glossary¶

Grid search is the baseline¶

If there are $n_j$ nodes for continuous action $j$, grid search evaluates a candidate count proportional to

at every state cell. Total work therefore still covers the complete represented action support. Eligible JIT solve-value routes—ordinary singleton hard max, collective hard max, and singleton EV1 expected max—evaluate bounded C-order action blocks. Same-period value references, gated-target continuations, and edge-reference mappings are supported unchanged inputs to those blocks. Ordinary co-mapped state routes stream while preserving device-local continuation reads. Eligible singleton folded-state routes stream the action product at each shock node before the unchanged full-axis quadrature reduction. The classifier deliberately keeps co-map intersections with separate same-period or edge-reference channels, trivial action products, JIT-disabled and raw execution, and all simulation-policy construction dense. Collective EV1, EV1 with a fold, collective hard max with a fold, and EV1 without a discrete action are unsupported by the streamed program. See the canonical GridSearch route matrix. Streamed programs publish solve-time values (and collective dissolution flags), not replay or policy artifacts. The blockwise route does not establish a runtime or peak-memory improvement without measurement. Grid search is exact relative to its action grids, not to the underlying continuous choice set.

EGM replaces search with inversion¶

For a smooth liquid margin, EGM chooses an exogenous post-decision savings grid and inverts the Euler equation for consumption. That changes the dominant candidate growth from a current-state-by-action grid to a savings-grid construction plus interpolation. The gain comes from amortizing one inversion over current liquid states.

The gain disappears if the Euler right-hand side still varies arbitrarily with the current liquid state after conditioning on the solver’s rows. Declared intervals can sometimes recover amortization; otherwise grid search may be the better representation.

Envelopes recover non-concave choices¶

A discrete choice or a non-convex budget can produce several candidate value branches. DCEGM also supplies the general resources route when plain EGM is too narrow. When a discrete choice or non-convex schedule produces several branches, DCEGM and NBEGM construct them and take an upper envelope. Envelope configuration affects accuracy, topology handling, memory, and accelerator suitability; it is not cosmetic post-processing.

Nesting avoids a coupled two-dimensional inversion¶

NEGM and NNBEGM condition the liquid solve on candidates for an outer durable or illiquid post-decision state. They do not solve a genuinely coupled two-dimensional first-order-condition system. The outer candidate count therefore multiplies the cost of the complete inner solve, and batching or adaptive search can matter as much as the inner algorithm.

Read the detailed method pages:

• The endogenous-grid method

• Discrete choice and upper envelopes

• Nested endogenous-grid methods

• Declared non-convex budgets

• Scaling, memory, and hardware

For exact constructors and prerequisites, see Solvers and capabilities.

Related pages¶

• Guide: Choosing a solver and Authoring for EGM-family solvers

• Methods: The endogenous-grid method, Nested endogenous-grid methods, and Declared non-convex budgets

• Examples: Curated examples

• Reference: Solvers and capabilities