HPR Solver

Solve Linear Programming problems using HPR solver.

Trigger

When user wants to solve an LP problem (MPS file or natural language description).

Usage

For MPS Files

User provides path to .mps file. Confirm parameters first:

⚠️ Please confirm parameters:
1. stoptol (default 1e-6): ?
2. time_limit (default 3600s): ?
3. device_number (0=GPU, -1=CPU): ?
4. Need variable values? (Yes/No)

After confirmation, run:

~/julia/julia-1.10.4/bin/julia --project ~/.openclaw/workspace/HPR-LP \
  ~/.openclaw/workspace/HPR-LP/hprlp_solve.jl <mps_file> <time_limit> <stoptol> <device>

For Natural Language

Parse problem, output mathematical model for confirmation:

📐 Mathematical Model:

```max
[objective function]

[constraint 1]
[constraint 2]
[constraint 3]

Variables:

x₁ = [description]
x₂ = [description]


2. After user confirms, ask parameters (same as MPS)

3. Model in Julia/JuMP:

```julia
using JuMP
using HPRLP

model = Model(HPRLP.Optimizer)
set_optimizer_attribute(model, "stoptol", <value>)
set_optimizer_attribute(model, "time_limit", <value>)
set_optimizer_attribute(model, "device_number", <value>)
set_optimizer_attribute(model, "verbose", true)

@variable(model, x1 >= 0)
@variable(model, x2 >= 0)

@constraint(model, c1, <constraint 1>)
@constraint(model, c2, <constraint 2>)

@objective(model, Max, <objective>)

optimize!(model)

Output Solution Summary:

📊 HPR-LP Results

=== Solution Summary ===
Status: [OPTIMAL/INFEASIBLE/...]
Iterations: <count>
Solve Time: <seconds>
Primal Objective: <value>
Dual Objective: <value>
KKT Error: <error>

=== Variables ===
x₁ = <value>
x₂ = <value>

Parameters

| Parameter | Default | Description | |-----------|---------|-------------| | stoptol | 1e-6 | Stopping tolerance | | time_limit | 3600 | Time limit (seconds) | | device_number | 0 | GPU device (-1 for CPU) |

Non-LP Problems

If problem is NOT linear (has integer vars, x², products, etc.), respond:

⚠️ HPR only supports Linear Programming (LP).

This appears to be:
- Integer/MILP (use GLPK, CBC, HiGHS)
- Non-linear (use Ipopt)
- Quadratic (use Gurob, CPLEX)

Requirements

Julia 1.10.4
HPR-LP
Linux/macOS/Windows