MPBNGCInterface.jl

MPBNGCInterface.jl is a Julia module that interfaces the Fortran77 code Multiobjective Proximal Bundle Method MPBNGC.

The Multiobjective Proximal Bundle Method MPBNGC can be applied to the nonsmooth, nonconvex multiobjective optimization problem

	min f₁(x), ..., fₘ(x) 
	s.t. 	x ∈  Rⁿ, 
	 	lb ≤ x ≤  ub,
		lbc ≤ C' x ≤ ubc, 
		fᵢ(x) ≤ 0,		i = m+1, ..., m+ngcon,

where n, m, nlin, ngcon is the number of optimization variables, objective functions, linear constraints, general constraints, respectively. lb and ub are lower and upper bounds on x, lbc and ubc are lower and upper bounds on C' x, C is a n x nlin-matrix, fᵢ are objective and general constraint functions, and C' is the transposed of C.

Installation

You can install MPBNGCInterface.jl through the Julia Package Manager by executing the following command in the Pkg REPL:

add https://github.com/milzj/MPBNGCInterface.jl.git

The command should download the module and compile the Bundle method if you have gfortran installed.

The code build.jl located in deps when executed attempts to download the source code of the Proximal Bundle Method MPBNGC and tries to compile it together with its dependencies.

To run the tests, we can then execute in the Pkg REPL,

test MPBNGCInterface

The module is an unregistered Julia package. It has successfully been tested on Linux and Mac OS using Travics CI with julia version 1.0.5, 1.1.1, 1.2.0 and 1.3.1. Moreover, it has been tested on Windows 10 Education (version 10.0.16299) (64bit) with julia version 1.3.1 and gfortran of mingw-w64 (x86_64).

Compilation with gfortan

This code uses gfortran to compile the Proximal Bundle Method MPBNGC.

The interface does not support compilers other than gfortan.

Custom Installation

You can download the Proximal Bundle Method MPBNGC manually and use your favourite compiler flags to compile and build mpbngc.f together with its dependences.

You would need to create a shared library and place it in the subdirectory deps/usr.

Manual

There is no user manual or help file available for the module. I recommend to have a look at the examples and tests to figure out how to use the module.

The objective and constraint functions fᵢ need to implemented in a single function having the following signature:

function fasg!(n::Int64, x::Vector{Float64}, mm::Int64, 
		f::Vector{Float64}, g::Matrix{Float64})

even if you consider a single objective optimization problem. Function and subgradient evaluations are stored in f (a vector of length mm) and g (a matrix of size n x mm), respectively. f[1:m] are the objective function values and f[m+1:mm] the general constraint function values. ("!" is optional.)

If you consider a bound-constrained optimization problem, the "types" of the bounds lb and ub are stored in ib. Meaning, the components of ib indicate whether the corresponding component of x is unconstrained, fixed, bounded from below and/or bounded from above. The "classification" is performed by the function classify_bounds called by the inner constructor of the mutable struct BundleProblem according to the rules indicated in the documentation of the function classify_bounds (see src/Bounds.jl). The variable ib matches the input variable IX of the Fortran code of the bundle method.

You can modify ib before calling solveProblem, which calls the Fortran implemenation of the Proximal Bundle Method MPBNGC.

The bounds lbc and ubc (if present) get "classified" similarly via the same function. The types are stored in ic corresponding to the input variable IC of the Fortran code.

References

A user manual for the Proximal Bundle Method MPBNGC is provided in

M.M. Mäkelä: Multiobjective proximal bundle method for nonconvex nonsmooth optimization: Fortran subroutine MPBNGC 2.0. Reports of the Department of Mathematical Information Technology, Series B. Scientific Computing B 13/2003, University of Jyväskylä, Jyväskylä (2003)

Further details are provided in

M.M. Mäkelä, N. Karmitsa, O. Wilppu: Proximal Bundle Method for Nonsmooth and Nonconvex Multiobjective Optimization in Mathematical Modeling and Optimization of Complex Structures. T. Tuovinen, S. Repin and P. Neittaanmäki (eds.), Vol. 40 of Computational Methods in Applied Sciences, pp. 191--204, Springer, 2016.

Acknowledgments

I would like to thank Professor Marko M. Mäkelä for making the source code of the Proximal Bundle Method MPBNGC available online. I would like to acknowledge Prof. Dr. Michael Ulbrich and Dr. Christian Ludwig for explaining me how to interface Fortran code. I appreciate very much that Christian took time to meet with me and to answer questions I had about interfacing Fortran(77) code, and that he has allowed me to reuse large parts of his ODEInterface.jl code.

Author

The module has been implemented by Johannes Milz.