Global Optimization

Global Search, As Timely As Ever

``Consider everything. Keep the good. Avoid evil whenever you notice it.''
(1 Thess. 5:21-22)

New - COCONUT - GloptLab
Introduction - Techniques
Software (global) - Software (local) - Test Problems
Applications - Other Optimization - Related Topics
People - Open Positions in Global Optimization

Bulgarian translation -- Belorussian translation

This is a comprehensive archive of online information on (almost exclusively non-commercial) global optimization, and somewhat less comprehensive on local optimization, collected by Arnold Neumaier on the web server of the Computational Mathematics group at the University of Vienna, Austria. Later on this page there is a Table of Contents of this Site.

Please help to keep the archive up to date by informing me at about new or missing electronic documents related to public domain work on global optimization, and about links that are no longer working.

Related, but not formally part of this site are two other sites maintained by our research group in Vienna:

  • The GICOLAG web site, featuring the slides of most talks of the visiting and research program ''Global Optimization - Integrating Convexity, Optimization, Logic Programming, and Computational Algebraic Geometry'', held by the International Erwin Schrödinger Institute for Mathematical Physics (ESI) Vienna, Austria from October 1 - December 23, 2006. The slides give an accurate snapshot of the state of the art in complete global optimization as of December 2006.

  • The COCONUT web site with many links specifically devoted to the activities of the European COCONUT project, with the goal of integrating various existing complete approaches to global optimization into a uniform whole, and a current follow-up project.

    Open Positions in Global Optimization

    Past Positions in Global Optimization

    New New New New New New New

    LINCOA, LINearly Constrained Optimization Algorithm
    for up to a few hundred variables (in Fortran 77, by Mike Powell)

    Comparison of derivative-free optimization algorithms (2012, by Nick Sahinidis)

    Black-Box Optimization Benchmarking (BBOB) 2012 (by Auger, Hansen, et al.)

    Projective methods for constraint satisfaction and global optimization (slides of a lecture at ISMP2012)

    Structure-driven methods for large-scale optimization

    VXQR1, Derivative-free unconstrained optimization based on QR factorizations (by Arnold Neumaier)

    IGPE - Incremental Global Parameter Estimation, for the global estimation of parameters in dynamical systems.

    GloptLab, an easy-to-use testing and development platform for solving quadratic constraint satisfaction problems, written in Matlab. All implemented methods are rigorous, hence it is guaranteed that no feasible point is lost.

    BMIBNB, Global solver for nonconvex problems in the YALMIP modeling environment (in Matlab, by Johan Löfberg)

    Black Box Optimization with Data Analysis for the global optimization of smooth problems with expensive objective and/or constraints (by Kevin Kofler)

    25 difficult global optimisation problems related to spaceraft interplanetary trajectory optimisation

    Global optimization and constraint satisfaction (slides of my GICOLAG talk)

    The 2006 Beale-Orchard-Hays Prize for Excellence in Computational Mathematical Programming went to Nick Sahinidis and Mohit Tawarmalani for their paper describing the global optimization package BARON

    LaGO, Branch and Cut algorithm for nonconvex mixed integer nonlinear programs

    GICOLAG, Global Optimization - Integrating Convexity, Optimization, Logic Programming, and Computational Algebraic Geometry, A visiting and research program by the International Erwin Schrödinger Institute for Mathematical Physics (ESI) Vienna, Austria, October 1 - December 23, 2006

    The NEOS Server offers BARON for the solution of global optimization problems in GAMS format (excellent package!)

    Constrained global optimization (pdf, 225K), slides of a lecture (by Arnold Neumaier)

    RSOLVER (by Stefan Ratschan)
    for solving quantified inequality constraints. Examples include: projecting the solution set of a set of inequality constraints to two dimensions.

    Books and papers on global optimization (Google scholar search)

    Online Papers in Global Optimization (a random collection of about 300 papers)

    ICOS, rigorous complete solver for continuous constraint satisfaction problems

    Comparison of Global Solvers
    Within the COCONUT project, we performed extensive tests of the global solvers BARON, GlobSol, ICOS, LGO, LINGO, OQNLP, Premium Solver, MINOS, and COCOS (the solver in the alpha test version of the COCONUT environment) for various sublibraries of the COCONUT benchmark.

    SNOBFIT, MATLAB 6 package for the robust and fast solution of optimization problems with continuous variables varying within bound, possibly subject to additional soft constraints

    W. Huyer, A comparison of some algorithms for bound constrained global optimization, Manuscript (2004). (pdf file, 69K)
    The paper contains comparisons of the three heuristic global optimization programs MCS, Global, PGSL, using black box function evaluation only.

    The COCONUT environment is publicly available in an alpha test version since March 20, 2004.

  • A. Neumaier, Complete Search in Continuous Global Optimization and Constraint Satisfaction, pp. 271-369 in: Acta Numerica 2004 (A. Iserles, ed.), Cambridge University Press 2004.
    This almost book-sized survey covers the state of the art of techniques for solving general purpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete techniques that provably find all solutions (if there are finitely many). The core of the material is presented in sufficient detail that the survey may serve as a text for teaching constrained global optimization.

  • Fortran 95 version (adapted by Alan Miller) of the clustering global optimization program Global in Fortran 77 and C (by Tibor Csendes)

  • Constraint satisfaction and global optimization in robotics (slides of a talk, in pdf)

    Since starting this optimization page (September 1, 1995), this page was accessed steadily by about 30-40 different computers per day (last counted in 1999).

    Updates to the contents are made quite frequently. I try to keep a complete coverage of public domain work on continuous global optimization; many references to combinatorial and local optimization are included for my (and your) convenience, but there I don't aim at completeness. Thanks to all who helped me by providing useful information.

    The archive was reorganized on November 12, 1996; it now contains more than 1000 links to sources outside our server.

    Please write me to if your own work is not referenced, if you know some other useful link to public domain work that is missing here, or if you find any invalid links.

    If you do lots of computer work, prevent Computer Related Repetitive Strain Injuries by improving your typing habits.

    In the following table of contents, italic headings correspond to different files, while roman headings correspond to sections within a file. There are further files not in this table of contents, accessible through links given in individual files.

    Introduction to Global Optimization

    Global Optimization Techniques
    Global Optimization Software
    Local Optimization Software
    Optimization Test Problems
    Global Optimization Test Results
    People in Global (and Local) Optimization
    Applications of Optimization
    More Global (and Local) Optimization
    Topics related to Optimization

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