slsqp4j

Slsqp4j is a Java wrapper around the popular SLSQP nonlinear optimizer included in SciPy. The API mimics SciPy's in order to ease the translation of problems from Python to the JVM.

The bulk of the solving is done in slsqp.f90 which was written by Dieter Kraft and described in [1] & [2].

Building

Building Slsqp4j depends on both gcc and gfortran.

Ubuntu

You can install both with the command sudo apt install gcc gfortran. Additionally, your JAVA_HOME must point to your JDK install directory.

To build Slsqp4j, simply run gradle clean build in the project root directory.

Mac OSX

This procedure has been tested with adoptopenjdk8 ( brew tap AdoptOpenJDK/openjdk && brew install --cask adoptopenjdk8 ) on BigSur.

You can install both with the command brew install gradle gcc gfortran.

Additionally, your JAVA_HOME must point to your JDK real install directory (ie a path like /Library/Java/JavaVirtualMachines/adoptopenjdk-8.jdk/Contents/Home/ and not a path like /Library/Internet Plug-Ins/JavaAppletPlugin.plugin/Contents/Home that doesn't contain the include library.

To build Slsqp4j, simply run gradle clean build in the project root directory.

Errors & solutions: /usr/local/Cellar/gcc/10.2.0/lib/gcc/10/gcc/x86_64-apple-darwin19/10.2.0/include-fixed/stdio.h:78:10: fatal error: _stdio.h: No such file or directory 78 | #include <_stdio.h> | ^~~~~~~~~~ compilation terminated. ==> run xcode-select --install Then run XCode and install additional components

Windows

(Note: The following steps were performed using scoop command-line installer.)

You can install both with the command scoop install mingw-winlibs. Additionally, your JAVA_HOME must point to your JDK install directory.

To build Slsqp4j, simply run gradle clean build in the project root directory.

Usage

Create an objective function that implements the Vector2ScalarFunc interface:

    public static class ObjectiveFunction implements Vector2ScalarFunc
    {
        @Override
        public double apply(double[] x, double... arg)
        {
            // for example
            return x[0] * x[1];
        }
    }

Specify one or more constraints:

    public static final class VectorConstraintFunction implements Vector2VectorFunc
    {
        @Override
        public double[] apply(double[] x, double... arg)
        {
            return new double[] {x[0] - x[1]};
        }
    }

    final VectorConstraint constraint = new VectorConstraint.VectorConstraintBuilder()
        .withConstraintType(ConstraintType.EQ)
        .withConstraintFunction(new VectorConstraintFunction())
        .build();

To perform the optimization, you must construct an instance of an Slsqp object. You do this using the Builder pattern:

final Slsqp slsqp = new Slsqp.SlsqpBuilder()
    .withObjectiveFunction(new ObjectiveFunction())
    .addVectorConstraint(constraint)
    .build();

Then simply call optimize passing in an initial guess vector:

final OptimizeResult result = slsqp.minimize(new double[] {1, -1});

The returned OptimizeResult contains information about the state of the solver. If result.success() returns true, the solver is complete and the vector contained in result.resultVec() is the point at which the function is minimized.

Below is a comparison showing the complete usage of Slsqp4j's API vs. SciPy's optimize API.

Slsqp4j

final VectorConstraint constraint = new VectorConstraint.VectorConstraintBuilder()
    .withConstraintType(ConstraintType.EQ)
    .withConstraintFunction((x, arg) -> x[0] - x[1])
    .build();
final Slsqp slsqp = new Slsqp.SlsqpBuilder()
    .withObjectiveFunction((x, arg) -> x[0] * x[1])
    .addVectorConstraint(constraint)
    .build();
final OptimizeResult result = slsqp.minimize(new double[]{1, -1});

SciPy

res = minimize(lambda d: d[0] * d[1], [1, -1], method='SLSQP', 
        constraints={'type': 'ineq', 'fun': lambda x: x[0] - x[1]})

The API is slightly more verbose than SciPy's one due to Java's type safety, but the similarities should hopefully be apparent. For more usage examples refer to the tests in SlsqpTests.java. For a complete list of the SlsqpBuilder parameters consult the documentation in Slsqp.java.

Thread Safety

Since the SLSQP algorithm is iterative, it is assumed that an instance of Slsqp will not be shared among threads, thus instances are not thread-safe. Rather, an instance of Slsqp should be constructed once, with the parameters of the optimization problem given to the builder, and then repeated calls to slsqp.optimize() should be made until a value of true is returned on a call to success() on the returned OptimizeResult instance.

Tests

The majority of the tests in SlsqpTests.java were ported from SciPy's SLSQP tests.

License

Slsqp4j is released under the BSD license.

References

1. Dieter Kraft, "A software package for sequential quadratic programming", Technical Report DFVLR-FB 88-28, Institut für Dynamik der Flugsysteme, Oberpfaffenhofen, July 1988.
2. Dieter Kraft, "Algorithm 733: TOMP–Fortran modules for optimal control calculations," ACM Transactions on Mathematical Software, vol. 20, no. 3, pp. 262-281 (1994).