# nimopt

> An LP/MILP builder in which a variable is a dimension. A constraint is
> an array over its free sets crossed with the column space, so the array
> is the matrix. nimblend, the labeled sparse array it is built on, is
> documented under its own section.

## For agents

- [For agents](/for-agents): The mental model, the public surface, and the mistakes to avoid when writing nimopt.
- [nimopt](/): An LP/MILP builder in which a variable is a dimension. Models are declared over named index sets and solutions are returned over the same sets.

## Get started

- [Get started](/get-started): Install nimopt, build a transport model, solve it, and read the solution back over its index sets.

## Vocabulary

- [Vocabulary](/vocabulary): The terms used throughout the documentation, each defined once.

## Reference

- [Constraint](/reference/constraint): The rows an expression produces, the right-hand side that bounds them, and the conditions that shape them.
- [Definition](/reference/definition): The symbols and constraints a model is written from, declared before any data exists.
- [Explanation](/reference/explanation): The shape of what is declared and, where it is built, of what was built from it.
- [Expressions](/reference/expression): Terms, the frame they share, the sums that reduce them and the relations that bound them.
- [Files](/reference/files): The file a definition or a model writes, the meaning of each key, the two data sources, and the functions that read and write it.
- [Row and Absence](/reference/inspection): What one row of a built model contains, and which coordinates were dropped from a constraint.
- [Model](/reference/model): The model that contains the columns, the rows and the objective, and the matrix it assembles.
- [Param](/reference/param): Coefficients over a set product, from a dense array or from label columns.
- [Sets and domains](/reference/sets): Name a dimension, give it a second name, and list which members of a product a model uses.
- [Solution](/reference/solution): Status, objective, primals and duals, returned over the sets they were declared over.
- [Solvers](/reference/solvers): What each solver adapter can do, the options a caller can set, and a session that keeps one solver open.
- [Variable](/reference/variable): A variable over a set product, the columns it occupies, and the reserved dimension names.

## nimblend

- [nimblend arrays](/nimblend/arrays): The array contract, the two implementations behind it, and what an absence declaration means.
- [nimblend domains](/nimblend/domains): The coordinates an array has, the three ways a position is computed, and the buffer assembly writes into.
- [nimblend](/nimblend): A labeled sparse N-dimensional array library, and the layer nimopt's matrices are built on.

## Explanation

- [A variable is a dimension](/explanation/a-variable-is-a-dimension): Why the column space is a dimension, and why nothing stores a column index.
- [Expressions are symbolic](/explanation/expressions-are-symbolic): What an expression stores before it is materialised, and what materialising it does.
- [The array is the matrix](/explanation/the-array-is-the-matrix): Why a constraint needs no assembly step, and what a model's build does.
- [The package boundary](/explanation/the-package-boundary): What belongs to nimblend, what belongs to nimopt, and the tests that keep the boundary where it is.
- [What the numbers measure](/explanation/what-the-numbers-measure): The benchmark figures, what each is measured against, and what none of them claims.

## Tutorial

- [Sets and parameters](/tutorial/sets-and-parameters): Declare the index sets of the transport model and the data indexed over them.
- [Variables](/tutorial/variables): Declare the shipment variable over plants and warehouses, and set its bounds and integrality.
- [Expressions](/tutorial/expressions): Write the sums the constraints and the objective are written over, without computing anything.
- [Constraints](/tutorial/constraints): Add the supply and demand constraints, and see how many rows each family produces.
- [Solving](/tutorial/solving): Set the objective function, call the solver, and check the status before reading values.
- [Reading the solution](/tutorial/reading-the-answer): Read primal and dual values over their index sets, and the distinction between an absent value and a zero.

## Guides

- [Declaring a model at scale](/guides/at-scale): Read a model's shape as it is declared, build the matrix once, and read a large solution.
- [Bounds from a parameter](/guides/bounds-from-parameters): Give each column its own bound from a parameter, broadcast over the dimensions the parameter lacks.
- [Coefficient arithmetic](/guides/coefficient-arithmetic): Combine parameters into a coefficient, divide by a parameter, add a constant, and the forms that raise with the form to write instead.
- [Conditions on a sum and on a constraint](/guides/conditions): Restrict the members a sum runs over, restrict the rows a constraint produces, or declare the rows explicitly.
- [A member fixed at a label](/guides/fixed-members): Reference one member of a dimension by its label, removing that dimension from the frame.
- [Interior point and first-order methods](/guides/highs-methods): The HiGHS simplex, IPX, HiPO and PDLP methods through the options of nimopt, the memory each requires, and how to install a HiGHS with HiPO and GPU support.
- [Lags](/guides/lags): Reference a variable at the previous or next member of a set, and choose whether the boundary row is dropped or wraps around.
- [Piecewise-linear curves](/guides/piecewise): Relate one expression to another through breakpoints, with an exact integer formulation or a tangent formulation, and save the declaration in a model file.
- [Saving and loading a model](/guides/saving-and-loading): Write a definition or a built model to a file in the expression syntax of nimopt, read it back, and store the data inline or beside it.
- [A variable over a subset](/guides/subsets): Declare a variable over the members of a set product that exist in the model, leaving the others with no column.

## Worked models

- [Commitment](/models/commitment): Unit commitment with a binary on-off column per generator and snapshot.
- [Dispatch](/models/dispatch): Least-cost dispatch of a generator fleet against a load. The baseline formulation.
- [Expansion](/models/expansion): "A two-stage stochastic program: capacity chosen before the scenario is known, dispatched once it is."
- [Fleet](/models/fleet): The dispatch model declared as one variable per unit, instead of one variable over a product.
- [Worked models](/models): Ten complete models, each with its formulation, its data at any scale, and an independently computed reference objective.
- [Nodal](/models/nodal): Generators sited at buses, grouped into bus balance rows by a lookup parameter.
- [Profiled](/models/profiled): A dispatch whose capacity is a profile, with one bound per generator and hour.
- [Recourse](/models/recourse): "Stochastic unit commitment: a binary on-off decision fixed before the scenario is known."
- [Sector](/models/sector): Technologies sited in some regions, running in every hour. Sparse in one axis, dense in the other.
- [Storage](/models/storage): A generator fleet and batteries meeting an hourly load, with the hours coupled through the stored energy.
- [Transport](/models/transport): Plants shipping to warehouses over a network that is not complete.