Abstract
The Lipschitz Global Optimizer (LGO) software integrates global and local scope search methods, to handle a very general class of nonlinear optimization models. Here we discuss the LGO implementation linked to the General Algebraic Modeling System (GAMS). First we review the key features and basic usage of the GAMS /LGO solver option, then present reproducible numerical results to illustrate its performance.
Similar content being viewed by others
References
Ali M.M., Khompatraporn Ch., Zabinsky Z.B. (2005) A numerical evaluation of several global optimization algorithms on selected benchmark test problems. J. Global Optim. 31, 635–672
Aris R. (1999) Mathematical Modeling: A Chemical Engineer’s Perspective. Academic Press, San Diego, CA
Bartholomew-Biggs M. (2005) Nonlinear Optimization with Financial Applications. Kluwer Academic Publishers, Dordrecht
Benson, H.P., Sun, E.: LGO—Versatile tool for global optimization. ORMS Today 27(5), 52–55 (2000) see http://www.lionhrtpub.com/orms/orms-10-00/swr.html
Bliek, Ch., Spellucci, P., Vicente, L.N., Neumaier, A., Granvilliers, L., Monfroy, E., Benhamou, F., Huens, E., Van Hentenryck, P., Sam-Haroud, D., Faltings, B.: Algorithms for Solving Nonlinear Constrained and Optimization Problems: The State of the Art. COCONUT Project Report (2001) For further information on the COCONUT Project, including this downloadable report, see http://www.mat. univie.ac.at/~neum/glopt/coconut/index.html.
Bracken J., McCormick G.P. (1968) Selected Applications of Nonlinear Programming. Wiley, New York
Brooke A., Kendrick D., Meeraus A. (1988) GAMS: A User’s Guide. The Scientific Press, Redwood City, CA
Bussieck, M.R., Drud, A.S., Meeraus, A., Pruessner, A.: Quality assurance and global optimization. Presented at the 1st International Workshop on Global Constrained Optimization and Constraint Satisfaction COCOS 2002, Valbonne, France (2003)
Castillo, I.: Maple 10 and the Global Optimization Toolbox. ORMS Today 32(6), 56–60 (2005) see http://www.lionhrtpub.com/orms/orms-12-05/swr.html
Castillo, I., Kampas, F.J., Pintér, J.D.: Solving circle packing problems by global optimization: numerical results and industrial applications. (Submitted for publication) (2005)
Chong E.K.P., Zak S.H. (2001) An Introduction to Optimization, 2nd edn. Wiley, New York
Cogan, B.: How to get the best out of optimisation software. Sci. Comput. World 71, 67–68 (2003) see http://www.scientific-computing.com/scwjulaug03review_optimisation.html
Conn A., Gould N.I.M., Toint Ph.L. (1992) LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization. Springer-Verlag, Heidelberg
Diwekar U. (2003) Introduction to Applied Optimization. Kluwer Academic Publishers, Dordrecht
Dörner D. (1996) The Logic of Failure. Perseus Books, Cambridge, MA
Dolan E.D., Moré J.J. (2002) Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213
Drud, A.S.: CONOPT: A System for Large-Scale Nonlinear Optimization, Reference Manual for CONOPT Subroutine Library. ARKI Consulting and Development A/S, Bagsvaerd, Denmark (1996)
Edgar T.F., Himmelblau D.M., Lasdon L.S. (2001) Optimization of Chemical Processes, 2nd edn. McGraw-Hill, Boston
Ferris, M.C.: MATLAB and GAMS: Interfacing optimization and visualization software. Mathematical Programming Technical Report 98–19. University of Wisconsin, Wisconsin (2005) see http://www.cs. wisc.edu/math-prog/matlab.html.
Fletcher, R., Leyffer, S.: User Manual for filterSQP. Dundee University Numerical Analysis Report N/A 181 (1998)
Fletcher R., Leyffer S. (2002) Nonlinear programming without a penalty function. Math. Program. 91, 239–269
Floudas C.A. (1999) Deterministic Global Optimization: Theory, Algorithms, and Applications. Kluwer Academic Publishers, Dordrecht
Floudas C.A., Pardalos P.M., Adjiman C.S., Esposito W.R., Gumus Z.H., Harding S.T., Klepeis J.L., Meyer C.A., Schweiger C.A. (1999) Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, Dordrecht
Fourer, R.: Nonlinear Programming Frequently Asked Questions. Maintained by the Optimization Technology Center of Northwestern University and Argonne National Laboratory (2005) see http://www-unix.mcs.anl.gov/otc/Guide/faq/nonlinear-programming-faq.html
Frontline Systems: Premium Solver Platform—Field-Installable Solver Engines. Frontline Systems Inc., Incline Village, NV (2005) see http://www.solver.com
GAMS Development Corporation: GAMS. GAMS Development Corporation, Washington, DC (2005) see http://www.gams.com.
GAMS Global World: GLOBAL Library: A Collection of Nonlinear Programming Models (2005) see http://www.gamsworld.org/global/globallib.htm.
GAMS Performance World: PAVER—Automated Performance Analysis & Visualization (2005) see http://www.gamsworld.org/performance/paver.
Gershenfeld N. (1999) The Nature of Mathematical Modeling. Cambridge University Press, Cambridge
Gill P.E., Murray W., Saunders M.A. (2002) SNOPT: An algorithm for large-scale constrained optimization. SIAM J. Optim. 12, 979–1006
Gould, N.I.M., Orban, D., Toint, Ph.L.: GALAHAD—A library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. Technical Report RAL-TR-2002-014. Rutherford Appleton Laboratory, Chilton, Oxfordshire, England (2002)
Grossmann I.E. (ed) (1996) Global Optimization in Enginnering Design. Kluwer Academic Publishers, Dordrecht/Boston/London
Hansen P.E., Jørgensen S.E. (eds) (1991) Introduction to Environmental Management. Elsevier, Amsterdam
Henrion, D.: A review of the global optimization toolbox for maple. IEEE Control Syst. Mag. (To appear) (2006) Available online at http://www.laas.fr/~henrion/papers/mapleglobopt.pdf
Hillier F.J., Lieberman G.J. (2005) Introduction to Operations Research, 8th edn. McGraw-Hill, New York
Horst R., Pardalos P.M. (eds) (1995) Handbook of Global Optimization, vol. 1. Kluwer Academic Publishers, Dordrecht
Horst R., Tuy H. (1996) Global Optimization: Deterministic Approaches, 3rd edn. Springer-Verlag, Berlin
Isenor G., Pintér J.D., Cada M. (2003) A global optimization approach to laser design. Optim. Eng. 4, 177–196
Kalwelagen, E.: Interfacing GAMS with other applications. Tutorial and examples. GAMS Development Corporation, Washington, DC (2005) See http://www.gams.com/~erwin/interface/ interface.html
Kampas, F.J., Pintér, J.D.: Global optimization in Mathematica: a comparative numerical study. In: Proceedings of the 2005 Wolfram Technology Conference Champaign, IL, 2005. http://library.wolfram.com/infocenter/Conferences/5824/
Kampas F.J., Pintér J.D. (2006) Configuration analysis and design by using optimization tools in Mathematica. The Mathematica Journal 10, 128–154
Khompatraporn Ch., Pintér J.D., Zabinsky Z.B. (2005) Comparative assessment of algorithms and software for global optimization. J. Global Optim. 31, 613–633
Lasdon L.S., Smith S. (1992) Solving large sparse nonlinear programs using GRG. ORSA J. Comput. 4, 2–15
Leyffer, S., Nocedal, J. (eds.): Large scale nonconvex optimization. SIAG/OPT Views News (2003) Published by the SIAM Activity Group on Optimization (25 pages.) Available online at http://www.mat.uc.pt/siagopt/.
Liberti L., Maculan N. (eds)(2006) Global Optimization: From Theory to Implementation. Springer Science + Business Media, New York
LINDO Systems: LINDO Solver Suite. LINDO Systems Inc., Chicago, IL (2005) see www.lindo.com.
Lopez, R.J.: Advanced Engineering Mathematics with Maple. Electronic book edition published by Maplesoft Inc., Waterloo, ON (2005)
Maplesoft: Global Optimization Toolbox for Maple. Maplesoft Inc., Waterloo, ON (2004) see http://www.maplesoft.com/products/toolboxes/globaloptimization.
Maplesoft: Maple. Maplesoft Inc., Waterloo, ON (2005) see http://www.maplesoft.com.
(The) MathWorks: MATLAB. The MathWorks, Inc., Natick, MA (2004) see http:/www.mathworks.com
Maximal Software: MPL. Distributed by Maximal Software Inc. Arlington, VA (2005) see http://www.maximal-usa.com.
McCarl, B.A.: McCarl’s GAMS User Guide (2004) see http://www.gams.com/dd/docs/bigdocs/ gams2002/. (Current edition dated 2004.)
Melissen, J.B.M.: Packing and Covering with Circles. Ph.D. Dissertation, University of Utrecht, Utrecht (1997)
Mittelmann, H.D., Spellucci, P.: Decision Tree for Optimization Software (2005) see http:// plato.asu.edu/guide.html
Mittelmann H.D., Pruessner A. (2006) A server for automated performance analysis of benchmarking data. Optim. Methods Softw. 21, 105–120
Murray J.D. (1983) Mathematical Biology. Springer-Verlag, Berlin
Murtagh, B.A., Saunders, M.A.: MINOS 5.4 User’s Guide. Technical Report SOL 83-20R (Revised edn.) Department of Operations Research, Stanford University, Stanford, CA (1995)
Neumaier A. (2004) Complete search in continuous optimization and constraint satisfaction. In: Iserles A., (eds) Acta Numerica 2004. Cambridge University Press, Cambridge, pp. 271–369
Neumaier, A.: Global Optimization (2005a) see http://www.mat.univie.ac.at/~neum/ glopt.html.
Neumaier, A.: COCONUT Project (2005b) see http://www.mat.univie.ac.at/~neum/ glopt/coconut/ index.html.
Neumaier A., Scherbina O., Huyer W., Vinkó T. (2005) A comparison of complete global optimization solvers. Math. Program. 103, 335–356
Papalambros P.Y., Wilde D.J. (2000) Principles of Optimal Design. Cambridge University Press, Cambridge
Paragon Decision Technology: AIMMS. Paragon Decision Technology BV, Haarlem, The Netherlands (2005) see http://www.aimms.com.
Pardalos P.M., Resende M.G.H. (eds) (2002) Handbook of Applied Optimization. Oxford University Press, Oxford
Pardalos P.M., Romeijn H.E. (eds) (2002) Handbook of Global Optimization, vol. 2. Kluwer Academic Publishers, Dordrecht
Pintér J.D. (1996a) Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications). Kluwer Academic Publishers, Dordrecht
Pintér, J.D.: Continuous global optimization software: A brief review. Optima 52, 1–8 (1996b) see http://plato.la.asu.edu/gom.html.
Pintér J.D. (1997) LGO—A program system for continuous and Lipschitz optimization. In: Bomze I.M., Csendes T., Horst R., Pardalos P.M. (eds) Developments in Global Optimization. Kluwer Academic Publishers, Dordrecht, pp. 183–197
Pintér, J.D.: Computational Global Optimization in Nonlinear Systems—An Interactive Tutorial. Lionheart Publishing, Inc. Atlanta, GA (2001a) see http://www.lionhrtpub.com/books/globaloptimization.html.
Pintér J.D. (2001b) Globally optimized spherical point arrangements: model variants and illustrative results. Ann. Oper. Res. 104, 213–230
Pintér J.D. (2002) Global optimization: software, test problems, and applications. In: Pardalos P.M., Romeijn H.E.(eds) Handbook of Global Optimization, vol 2. Kluwer Academic Publishers, Dordrecht, pp. 515–569
Pintér, J.D.: GAMS/LGO (User Guide) (2003a) http://www.gams.com/solvers/lgo.pdf
Pintér J.D. (2003b) Globally optimized calibration of nonlinear models: techniques, software, and applications. Optim. Methods Softw. 18, 335–355
Pintér, J.D.: GAMS/LGO nonlinear solver suite: key features, usage, and numerical performance (2003c) http://www.gams.com/solvers/GAMS_LGO_paper.pdf
Pintér, J.D.: The Maple Global Optimization Toolbox. Technical report; downloadable from the product page (2004) http://www.maplesoft.com/products/toolboxes/globaloptimization.
Pintér, J.D.: LGO – A Model Development System for Continuous Global Optimization. User’s Guide. (Current revised edition.) Pintér Consulting Services, Inc., Halifax, NS (2005a)
Pintér J.D. (2005b) Nonlinear optimization in modeling environments: software implementations for compilers, spreadsheets, modeling languages, and integrated computing systems. In: Jeyakumar V., Rubinov A.M. (eds.) Continuous Optimization: Current Trends and Applications. Springer Science + Business Media, New York, pp. 147–173
Pintér, J.D.: AIMMS/LGO solver engine: a brief introduction and user’s guide (2005c) see http:// www. aimms.com/aimms/download/solvers/aimms_lgo_solver_engine_introduction_and_ user_guide.pdf
Pintér, J.D.: Nonlinear optimization with MPL/LGO: introduction and user’s guide. Distributed by Maximal Software, Inc., Arlington, VA, USA (2005d) www.maximal-usa.com.
Pintér J.D. (ed) (2006) Global Optimization—Scientific and Engineering Case Studies. Springer Science + Business Media, New York
Pintér, J.D., Holmström, K., Göran, A.O., Edvall, M.M.: User’s Guide for TOMLAB/LGO. TOMLAB Optimization AB, Väster Sweden (2004). see http://tomlab.biz/docs/ TOMLAB_LGO.pdf
Pintér, J.D., Kampas, F.J.: MathOptimizer Professional—An Advanced Modeling and Optimization System for Mathematica, Using the LGO Solver Engine. User’s Guide. Pintér Consulting Services Inc., Halifax, NS (2003)
Pintér J.D., Kampas F.J. (2005) Nonlinear optimization in Mathematica with MathOptimizer Professional. Math. Educ. Res. 10(2): 1–18
Pintér J.D., Kampas F.J. (2006) MathOptimizer Professional: key features and illustrative applications. In: Liberti L., Maculan N. (eds) Global Optimization: From Theory to Implementation. Springer Science + Business Media, New York, pp. 263–280
Pintér J.D., Linder D., Chin P. (2006) Global Optimization Toolbox for Maple: an introduction with illustrative applications. Optim. Methods Softw. 21, 565–582
Pintér, J.D., Purcell, C.J.: Optimization of finite element models with MathOptimizer and Proceedings of the 2003 Mathematica Developer Conference, Champaign, IL. (2003) Available at http://library.wolfram.com/infocenter/Articles/5347/
Powell M.J.D. (2002) UOBYQA: unconstrained optimization by quadratic approximation. Math. Program. 92, 555–582
Schittkowski K. (2002) Numerical Data Fitting in Dynamical Systems. Kluwer Academic Publishers, Dordrecht
Specht, E.: www.packomania.com (2005)
Steeb W-H. (2005) The Nonlinear Workbook, 3rd edn. World Scientific, Singapore
Stojanovic S. (2003) Computational Financial Mathematics Using Mathematica. Birkhäuser, Boston
Stortelder W.J.H., de Swart J.J.B., Pintér J.D. (2001) Finding elliptic Fekete points sets: two numerical solution approaches. J. Comput. Appl. Math. 130, 205–216
Strongin R.G., Sergeyev Ya.D. (2000) Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht
Tawarmalani M., Sahinidis N.V. (2002) Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer Academic Publishers, Dordrecht
Tervo J., Kolmonen P., Lyyra-Laitinen T., Pintér J.D., Lahtinen T. (2003) An optimization-based approach to the multiple static delivery technique in radiation therapy. Ann. Oper. Res. 119, 205–227
TOMLAB Optimization: TOMLAB. TOMLAB Optimization AB, Väster Sweden (2005) http://www.tomlab.biz
Ugray, Z., Lasdon, L., Plummer, J., Glover, F., Kelly, J., Marti, R.: A multistart scatter search heuristic for smooth NLP and MINLP problems. INFORMS J. Comput. (To appear.) (2006). See http://www.utexas.edu/courses/lasdon/ijocmultistart5.htm.
Vanderbei R.J. (1999) LOQO User’s manual—version 3.10. Optim. Methods Softw. 12, 485–514
Waltz, R., Nocedal, J.: KNITRO 2.0 User’s Manual. Technical Report OTC 2003/05, Optimization Technology Center, Northwestern University, Evanston, IL (2003) see also Ziena Optimization, Inc. http://www.ziena.com/knitro/manual.htm.
Wass J.A. (2006) Global optimization with Maple. Sci. Comput. 24, 16
Wolfram Research: Mathematica. (2005) see http://www.wolfram.com/
Wright M.H. (1996) Direct search methods: once scorned, now respectable. In: Griffiths D.F., Watson G.A. (eds) Numerical Analysis 1995: Proceedings of the 1995 Biennial Conference on Numerical Analysis. Addison Wesley Longman Ltd, Reading, MA, pp. 191–208
Zabinsky Z.B. (2003) Stochastic Adaptive Search for Global Optimization. Kluwer Academic Publishers, Dordrecht
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pintér, J.D. Nonlinear optimization with GAMS /LGO. J Glob Optim 38, 79–101 (2007). https://doi.org/10.1007/s10898-006-9084-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9084-2