ipopt-net 3.14.19.13

IpoptNet

A modern .NET interface for IPOPT (Interior Point OPTimizer), a software library for large-scale nonlinear optimization. This library provides both a high-level modeling API with automatic differentiation and a low-level native wrapper.

Installation

Install the package via NuGet:

dotnet add package ipopt-net

The package includes native binaries for:

• Windows (x64)
• Linux (x64, requires libgfortran5 liblapack3 libblas3 libgomp1)

Features

• Modeling API: Define nonlinear optimization problems using C# expressions with natural syntax
• Automatic Differentiation: Gradients and Hessians computed automatically via reverse-mode AD
• Intelligent Matrix Caching: Automatically detects and pre-computes constant matrices for LP/QP/QCP problems
• High-level Wrapper: Clean, disposable IpoptSolver class for direct API access
• Native Performance: Uses .NET 10 LibraryImport for efficient C API calls
• Expression Support: Arithmetic, trigonometric, exponential, logarithmic, and power operations
• Flexible Constraints: Equality, inequality, and bound constraints

Quick Start (Modeling API)

The modeling API allows you to define optimization problems with automatic differentiation:

using IpoptNet.Modelling;

// Create a model
var model = new Model();

// Configure IPOPT (optional)
model.Options.LinearSolver = LinearSolver.PardisoMkl;
model.Options.HessianApproximation = HessianApproximation.LimitedMemory;

// Add variables with bounds and optional initial guesses
var x = model.AddVariable(1, 5);
var y = model.AddVariable(1, 5) { Start = 3.7 };
var z = model.AddVariable(1, 5);
var w = model.AddVariable(1, 5);

// Set objective: minimize x*w*(x+y+z) + z (expressions can be built incrementally)
var expr = x * (x + y + z);
expr *= w;
model.SetObjective(expr + z);

// Add constraints
model.AddConstraint(x * y * z * w >= 25);
model.AddConstraint(x*x + y*y + z*z + w*w == 40);

// Solve
var result = model.Solve();

if (result.Status == ApplicationReturnStatus.SolveSucceeded)
{
    Console.WriteLine($"x = {result.Solution[x]:F3}");
    Console.WriteLine($"y = {result.Solution[y]:F3}");
    Console.WriteLine($"z = {result.Solution[z]:F3}");
    Console.WriteLine($"w = {result.Solution[w]:F3}");
    Console.WriteLine($"Objective = {result.ObjectiveValue:F3}");
}

Output:

x = 1.000
y = 4.743
z = 3.821
w = 1.379
Objective = 17.014

Supported Operations

The expression system supports:

• Arithmetic: +, -, *, /, unary -
• Power: Expr.Pow(x, n), Expr.Sqrt(x)
• Trigonometric: Expr.Sin(x), Expr.Cos(x), Expr.Tan(x)
• Exponential/Log: Expr.Exp(x), Expr.Log(x)
• Constraints: >=, <=, ==

Performance Optimization

The solver automatically detects problem structure and optimizes matrix computations:

Constant Matrix Detection

For certain problem types, derivative matrices remain constant throughout the solution process. The library automatically detects these cases and pre-computes matrices once:

Example - Linear Program:

var model = new Model();
var x = model.AddVariable(0, 10);
var y = model.AddVariable(0, 10);

// Linear objective and constraints - matrices computed once
model.SetObjective(2*x + 3*y);
model.AddConstraint(x + 2*y <= 10);
model.AddConstraint(3*x + y <= 12);

var result = model.Solve();

Example - Quadratic Program:

var model = new Model();
var x = model.AddVariable();
var y = model.AddVariable();

// Quadratic objective, linear constraints - Hessian and Jacobian computed once
model.SetObjective(x*x + y*y - 4*x - 6*y);
model.AddConstraint(x + y <= 5);

var result = model.Solve();

This optimization is completely automatic - no code changes required. The solver analyzes the expression structure and applies the appropriate strategy.

More Examples

Rosenbrock Function (Unconstrained)

var model = new Model();
var x = model.AddVariable();
var y = model.AddVariable();

// Minimize (1-x)^2 + 100*(y-x^2)^2
model.SetObjective(Expr.Pow(1 - x, 2) + 100 * Expr.Pow(y - x*x, 2));

var result = model.Solve();
// Converges to x=1, y=1

Constrained Optimization

var model = new Model();
var x = model.AddVariable();
var y = model.AddVariable();

// Minimize x^2 + y^2
model.SetObjective(x*x + y*y);

// Subject to x + y = 4
model.AddConstraint(x + y == 4);

var result = model.Solve();
// Solution: x=2, y=2, objective=8

Trigonometric Optimization

var model = new Model();
var x = model.AddVariable(-Math.PI, Math.PI);

// Minimize -sin(x)
model.SetObjective(-Expr.Sin(x));

var result = model.Solve();
// Converges to x=π/2

Configuring IPOPT Options

The modeling API exposes all IPOPT configuration options through a strongly-typed API with enums:

var model = new Model();

// Configure solver options using enums (type-safe with IntelliSense)
model.Options.LinearSolver = LinearSolver.PardisoMkl;  // Use Intel MKL Pardiso
model.Options.HessianApproximation = HessianApproximation.Exact;
model.Options.MuStrategy = MuStrategy.Adaptive;

// Configure termination criteria
model.Options.Tolerance = 1e-7;
model.Options.MaxIterations = 100;
model.Options.MaxWallTime = 60.0;  // seconds

// Configure output verbosity
model.Options.PrintLevel = 5;  // 0=no output, 5=default, 12=verbose
model.Options.OutputFile = "ipopt.log";

// Configure NLP scaling
model.Options.NlpScalingMethod = NlpScalingMethod.GradientBased;

// Use custom options for advanced features
model.Options.SetCustomOption("bound_push", 0.01);
model.Options.SetCustomOption("acceptable_tol", 1e-5);

// Define and solve your problem...
// ...
var result = model.Solve();

Available Linear Solvers

• LinearSolver.Mumps - Default, included with IPOPT
• LinearSolver.PardisoMkl - Intel MKL Pardiso (included)
• LinearSolver.PardisoProject - Pardiso from pardiso-project.org (often faster, requires external library)
• LinearSolver.Ma27, Ma57, Ma77, Ma86, Ma97 - HSL solvers (require external library)
• LinearSolver.Wsmp - Watson Sparse Matrix Package (requires external library)
• LinearSolver.Spral - Sparse Parallel Robust Algorithms Library (requires external library)

Common Options

• Termination: Tolerance, MaxIterations, MaxWallTime, MaxCpuTime
• Output: PrintLevel, OutputFile, PrintUserOptions
• Algorithm: LinearSolver, HessianApproximation, MuStrategy
• Scaling: NlpScalingMethod, LinearSystemScaling
• Tolerances: ConstraintViolationTolerance, DualInfeasibilityTolerance

Low-level API

For advanced users who want direct control over the IPOPT solver:

using IpoptNet;

// Define callback functions
EvalFCallback evalF = (n, x, newX, objValue, userData) =>
{
    *objValue = x[0] * x[3] * (x[0] + x[1] + x[2]) + x[2];

    // Note: If a callback cannot be evaluated at a given point (e.g. division by zero), 
    // it should return false. IPOPT will then attempt to backtrack to a valid point.
    // If it cannot recover, the solve will terminate with InvalidNumberDetected.
    return true;
};

// Define gradient, constraint, Jacobian, and Hessian callbacks...

// Create solver
using var solver = new IpoptSolver(
    n: 4, xL, xU,
    m: 2, gL, gU,
    jacobianNonZeros, hessianNonZeros,
    evalF, evalGradF, evalG, evalJacG, evalH);

// Set options
solver.SetOption("print_level", 5);
solver.SetOption("tol", 1e-7);

// Solve
var x = new double[] { 1, 5, 5, 1 };
var status = solver.Solve(x, out var objValue);

Problem Formulation

IPOPT solves nonlinear optimization problems of the form:

minimize    f(x)
subject to  g_L ≤ g(x) ≤ g_U
            x_L ≤ x ≤ x_U

where:

• f(x) is the objective function
• g(x) are constraint functions
• x are the optimization variables
• Bounds can be infinite for unconstrained dimensions

References

• IPOPT Project: https://coin-or.github.io/Ipopt/
• IPOPT Documentation: https://coin-or.github.io/Ipopt/DOCUMENTATION.html
• IPOPT Paper: Wächter & Biegler (2006), "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming"

License

This .NET wrapper is provided as-is. IPOPT itself is released under the Eclipse Public License (EPL).

Acknowledgments

IPOPT is developed and maintained by the COIN-OR project. This wrapper provides a convenient .NET interface with automatic differentiation capabilities.