Input Methods Overview

HPRLP supports three different ways to specify and solve linear programming problems. Choose the method that best fits your workflow.

Quick Comparison

Method	Best For	Key Advantage	When to Use
JuMP Integration	Model building in Julia	High-level modeling language	Building models programmatically with algebraic syntax
MPS Files	Standard format files	Industry compatibility	Reading benchmarks or problems from other tools
Direct API	Matrix-based input	Full control, no overhead	Working with pre-built matrices or custom algorithms

Choosing Your Input Method

Use JuMP Integration if you:

✓ Want to build models using algebraic expressions
✓ Need a high-level, readable problem formulation
✓ Are familiar with optimization modeling languages (like AMPL, GAMS)
✓ Want to easily switch between different solvers
✓ Prefer working with variables, constraints, and objectives directly

Example use case: Building a production planning model where you define decision variables and constraints naturally.

using JuMP, HPRLP
model = Model(HPRLP.Optimizer)
@variable(model, x >= 0)
@variable(model, y >= 0)
@objective(model, Max, 3x + 5y)
@constraint(model, x + 2y <= 10)
optimize!(model)

→ See JuMP Integration Guide

Use MPS Files if you:

✓ Have problems in MPS format from benchmarks (NETLIB, MIPLIB, etc.)
✓ Need to read problems generated by other optimization tools
✓ Want to use standard LP test sets
✓ Are comparing solver performance on established benchmarks
✓ Receive problem files from collaborators or other software

Example use case: Solving benchmark problems from the NETLIB test set or problems exported from commercial optimization software.

using HPRLP
model = build_from_mps("path/to/problem.mps")
params = HPRLP_parameters()
result = optimize(model, params)

→ See MPS Files Guide

Use Direct API if you:

✓ Already have your problem in matrix form
✓ Need maximum performance (no modeling overhead)
✓ Are implementing custom algorithms or research code
✓ Work with problems generated from scientific computing
✓ Want precise control over the problem formulation
✓ Are integrating HPRLP into existing numerical code

Example use case: Solving LP subproblems in a decomposition algorithm where constraint matrices are built programmatically.

using HPRLP, SparseArrays
A = sparse([...])  # Your constraint matrix
model = build_from_Abc(A, c, AL, AU, l, u)
params = HPRLP_parameters()
result = optimize(model, params)

→ See Direct API Guide

Can I Use Multiple Methods?

Yes! You can use different input methods in the same project. For example:

Use JuMP for rapid prototyping, then switch to Direct API for production
Validate your Direct API implementation against MPS benchmark files
Build models in JuMP and export/import via MPS format

What's Next?

Choose your input method using the guide above
Configure solver parameters in the Parameters guide
Understand the results in the Output & Results guide

Standard Form

Regardless of input method, HPRLP internally solves problems in the standard form:

\[\begin{array}{ll} \min \quad & c^T x + c_0\\ \text{s.t.} \quad & AL \leq Ax \leq AU \\ & l \leq x \leq u \end{array}\]

JuMP automatically converts your model to this form
MPS files are parsed into this representation
Direct API lets you specify this form directly