Summary
We present a review of several professional software products that serve to analyze and solve nonlinear (global and local) optimization problems across a variety of hardware and software environments. The product versions discussed have been implemented for compiler platforms, spreadsheets, algebraic (optimization) modeling languages, and for integrated scientific-technical computing systems. The discussion highlights some of the key advantages of these implementations. Test examples, well-known numerical challenges and client applications illustrate the usage of the current software versions.
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Aris, R.: Mathematical Modeling: A Chemical Engineers Perspective. Academic Press, San Diego, CA (1999)
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms. Wiley, New York (1993)
Benson, H.P., Sun, E. LGO — Versatile tool for global optimization. In: OR/MS Today, 27, 52–55 (2000)
Bertsekas, D.P.: Nonlinear Programming (2nd Edition). Athena Scientific, Cambridge, MA (1999)
Boender, C.G.E., Romeijn, H.E. Stochastic methods. In: Horst and Pardalos (eds) Handbook of Global Optimization. Volume 1, pp. 829–869 (1995)
Bornemann, F., Laurie, D., Wagon, S., Waldvogel, J.: The SIAM 100-Digit Challenge. A Study in High-Accuracy Numerical Computing. SIAM, Philadelphia, PA (2004)
Bracken, J. and McCormick, G.P.: Selected Applications of Nonlinear Programming. Wiley, New York (1968)
Brooke, A., Kendrick, D. and Meeraus, A.: GAMS: A User’s Guide. The Scientific Press, Redwood City, CA. (Revised versions are available from the GAMS Corporation.) See also http://www.gams.com (1988)
Casti, J.L.: Searching for Certainty. Morrow & Co., New York (1990)
Cogan, B. How to get the best out of optimization software. In: Scientific Computing World, 71, 67–68 (2003)
Corliss, G.F., Kearfott, R.B. Rigorous global search: industrial applications. In: Csendes, T. (ed) Developments in Reliable Computing, 1–16. Kluwer Academic Publishers, Boston/Dordrecht/London (1999)
Coullard, C, Fourer, R., Owen, J.H. (eds): Annals of Operations Research, 104, Special Issue on Modeling Languages and Systems. Kluwer Academic Publishers, Boston/Dordrecht/London (2001)
Chong, E.K.P., Zak, S.H.: An Introduction to Optimization (2nd Edition). Wiley, New York (2001)
Diwekar, U.: Introduction to Applied Optimization. Kluwer Academic Publishers, Boston/Dordrecht/London (2003)
Edgar, T.F., Himmelblau, D.M., Lasdon, L.S. Optimization of Chemical Processes (2nd Edition). McGraw-Hill, New York (2001)
Eigen, M. and Winkler, R.: Das Spiel. Piper & Co., München (1975)
Fourer, R.: Nonlinear Programming Frequently Asked Questions. Optimization Technology Center of Northwestern University and Argonne National Laboratory, http://www-unix.mcs.anl.gov/otc/Guide/faq/nonlinear-programming-faq.html (2004)
Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL — A Modeling Language for Mathematical Programming. The Scientific Press, Redwood City, CA (Reprinted by Boyd and Fraser, Danvers, MA, 1996. See also http://www.ampl.com) (1993)
Frontline Systems: Premium Solver Platform — Solver Engines. User Guide. Frontline Systems, Inc. Incline Village, NV (See http://www.solver.com, and http://www.solver.com/xlslgoeng.htm) (2001)
Gershenfeld, N.: The Nature of Mathematical Modeling. Cambridge University Press, Cambridge (1999)
Grossmann, I.E. (ed): Global Optimization in Engineering Design. Kluwer Academic Publishers, Boston/Dordrecht/London (1996)
Hansen, P.E. and Jørgensen, S.E. (eds): Introduction to Environmental Management. Elsevier, Amsterdam (1991)
Hillier, F.J. and Lieberman, G.J. Introduction to Operations Research. (8th Edition.) McGraw-Hill, New York (2005)
Horst, R., Pardalos, P.M. (eds): Handbook of Global Optimization (Volume 1). Kluwer Academic Publishers, Boston/Dordrecht/London (1995)
Horst, R., Tuy, H.: Global Optimization — Determinsitic Approaches (3rd Edition). Springer-Verlag, Berlin / Heidelberg / New York (1996)
ILOG: ILOG OPL Studio and Solver Suite. http://www.ilog.com (2004)
Isenor, G., Pintér, J.D., Cada, M.: A global optimization approach to laser design. Optimization and Engineering 4, 177–196 (2003)
Jacob, C.: Illustrating Evolutionary Computation with Mathematica. Morgan Kaufmann Publishers, San Francisco (2001)
Kallrath, J. (ed): Modeling Languages in Mathematical Optimization. Kluwer Academic Publishers, Boston/Dordrecht/London (2004)
Kampas, F.J., Pinter, J.D.: Generalized circle packings: model formulations and numerical results. Proceedings of the International Mathematica Symposium (Banff, AB, Canada, August 2004)
Kampas, F.J., Pinter, J.D.: Configuration analysis and design by using optimization tools in Mathematica. The Mathematica Journal (to appear) (2004)
Kampas, F.J., Pintér, J.D.: Advanced Optimization: Scientific, Engineering, and Economic Applications with Mathematica Examples. Elsevier, Amsterdam (to appear) (2005)
Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer Academic Publishers, Boston/Dordrecht/London (1996)
Lafe, O.: Cellular Automata Transforms. Kluwer Academic Publishers, Boston / Dordrecht / London (2000)
Lahey Computer Systems. Fortran 90 User’s Guide. Lahey Computer Systems, Inc., Incline Village, http://www.lahey.com (2002)
LINDO Systems. Solver Suite. LINDO Systems, Inc., Chicago, IL. http://www.lindo.com (1996)
Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman & Co., New York (1983)
Maplesoft. Maple. (Current version: 9.5.) Maplesoft, Inc., Waterloo, ON. http://www.maplesoft.com (2004)
Maplesoft. Global Optimization Toolbox. Maplesoft, Inc. Waterloo, ON. http://www.maplesoft.com (2004)
Maros, I., Mitra, G. (eds): Annals of Operations Research, 58, Applied Mathematical Programming and Modeling II (APMOD 93) J.C. Baltzer AG, Science Publishers, Basel (1995)
Maros, I., Mitra, G., Sciomachen, A. (eds): Annals of Operations Research, 81, Applied Mathematical Programming and Modeling III (APMOD 95). J.C. Baltzer AG, Science Publishers, Basel (1997)
Mittelmann, H.D., Spellucci, P. Decision Tree for Optimization Software. http://plato.la.asu.edu/guide.html (2004)
Maximal Software. MPL Modeling System. Maximal Software, Inc. Arlington, VA. http://www.maximal-usa.com (2002)
Murray, J.D.: Mathematical Biology. Springer-Verlag, Berlin (1983)
Neumaier, A.: Global Optimization. http://www.mat.univie.ac.at/neum/glopt.html (2004)
Neumaier, A.: Complete search in continuous global optimization and constraint satisfaction. In: Iserles, A. (ed) Acta Numerica 2004. Cambridge University Press, Cambridge (2004b)
Papalambros, P.Y., Wilde, D.J.: Principles of Optimal Design. Cambridge University Press, Cambridge (2000)
Paragon Decision Technology: AIMMS (Current version 3.5). Paragon Decision Technology BV, Haarlem, The Netherlands. See http://www.aimms.com (2004)
Pardalos, P.M., Shalloway, D. and Xue, G.: Global minimization of nonconvex energy functions: molecular conformation and protein folding. In: DI-MACS Series, 23, American Mathematical Society, Providence, RI (1996)
Pardalos, P.M., Romeijn, H.E. (eds): Handbook of Global Optimization. Volume 2. Kluwer Academic Publishers, Boston/Dordrecht/London (2002)
Pinter, J.D.: Global Optimization in Action. Kluwer Academic Publishers, Boston / Dordrecht / London (1996)
Pinter, J.D.: Continuous global optimization software: A brief review. Optima, 52, 1–8 (1996) (Web version is available at: http://plato.la.asu.edu/gom.html)
Pintér, J.D.: LGO — A Program System for Continuous and Lipschitz Optimization. In: Bomze, I.M., Csendes, T., Horst, R. and Pardalos, P.M. (eds) Developments in Global Optimization, 183–197. Kluwer Academic Publishers, Boston/Dordrecht/London (1997)
Pintér, J.D.: Extremal energy models and global optimization. In: Laguna, M., González-Velarde, J-L., (eds) Computing Tools for Modeling, Optimization and Simulation, 145–160. Kluwer Academic Publishers, Boston/Dordrecht/London (2000)
Pintér, J.D.: Computational Global Optimization in Nonlinear Systems. Lionheart Publishing Inc., Atlanta, GA (2001)
Pintér, J.D.: Globally optimized spherical point arrangements: model variants and illustrative results. Annals of Operations Research 104, 213–230 (2001)
Pintér, J.D.: MathOptimizer — An Advanced Modeling and Optimization System for Mathematica Users. User Guide. Pinter Consulting Services, Inc., Halifax, NS (2002a) (For a summary, see also http://www.wolfram.com/products/applications/mathoptimizer/)
Pintér, J.D.: Global optimization: software, test problems, and applications. In: Pardalos and Romeijn (eds) Handbook of Global Optimization. Volume 2, 515–569 (2002)
Pintér, J.D.: (2003a) Globally optimized calibration of nonlinear models: techniques, software, and applications. Optimization Methods and Software, 18, 335–355 (2003)
Pintér, J.D.: GAMS /LGO nonlinear solver suite: key features, usage, and numerical performance. Submitted for publication. Downloadable at http://www.gams.com/solvers/lgo (2003)
Pintér, J.D.: LGO — A Model Development System for Continuous Global Optimization. Users Guide. (Current revision.) Pinter Consulting Services, Inc., Halifax, NS (2004) (For a summary, see http://www.pinterconsulting.com)
Pintér, J.D.: Applied Nonlinear Optimization in Modeling Environments. CRC Press, Baton Rouge, FL (2005) (To appear)
Pintér, J.D. (ed): Global Optimization — Selected Case Studies. Springer Science + Business Media, New York (2005) (To appear)
Pintér, J.D., Holmström, K., Goran, A.O., Edvall, M.M.: User’s Guide for TOMLAB /LGO. TOMLAB Optimization AB, Västerås, Sweden (2004) (See http://www.tomlab.biz)
Pintér, J.D., Kampas, F.J.: MathOptimizer Professional — An Advanced Modeling and Optimization System for Mathematica Users with an External Solver Link. User Guide. Pinter Consulting Services, Inc., Halifax, NS, Canada (2003) (For a summary, see also http://www.wolfram.com/products/applications/mathoptpro/)
Pintér, J.D., Kampas, F.J.: Model development and optimization with Mathematica. In: Golden, B., Raghavan, S., Wasil, E. (eds) The Next Wave in Computing, Optimization, and Decision Technologies, 285–302. Springer Science + Business Media, New York (2005)
Pintér, J.D., Purcell, C.J.: Optimization of finite element models with MathOptimizer and ModelMaker. Lecture presented at the 2003 Mathematica Developer Conference, Champaign, IL (2003) (Extended abstract is available upon request, and also from http://www.library.com)
Ratschek, H., Rokne, J.: Experiments using interval analysis for solving a circuit design problem. Journal of Global Optimization 3, 501–518 (1993)
Ratschek, H., Rokne, J.: Interval methods. In: Horst and Pardalos (eds) Handbook of Global Optimization. Volume 1, 751–828 (1995)
Rich, L.G.: Environmental Systems Engineering. McGraw-Hill, Tokyo (1973).
Schittkowski, K.: Numerical Data Fitting in Dynamical Systems. Kluwer Academic Publishers, Boston/Dordrecht/London (2002)
Schroeder, M.: Fractals, Chaos, Power Laws. Freeman & Co., New York (1991)
Stewart, I.: Nature’s Numbers. Basic Books / Harper and Collins, New York (1995)
Stortelder, W.J.H., de Swart, J.J.B., Pintér, J.D.: Finding elliptic Fekete point sets: two numerical solution approaches. Journal of Computational and Applied Mathematics, 130, 205–216 (2001)
Tawarmalani, M., Sahinidis, N.V.: Convexification and Global Optimization in Continuous and Mixed-integer Nonlinear Programming. Kluwer Academic Publishers, Boston/Dordrecht/London (2002)
Tervo, J., Kolmonen, P., Lyyra-Laitinen, T., Pinter, J.D., and Lahtinen, T. An optimization-based approach to the multiple static delivery technique in radiation therapy. Annals of Operations Research, 119, 205–227 (2003)
TOMLAB Optimization. TOMLAB. TOMLAB Optimization AB, Västerås, Sweden (2004) (See http://www.tomlab.biz)
Trefethen, L.N.: The hundred-dollar, hundred-digit challenge problems. SIAM News, Issue 1, p. 3 (2002)
The MathWorks: MATLAB. (Current version: 6.5) The MathWorks, Inc., Natick, MA (2004) (See http://www.mathworks.com)
Vladimirou, H., Maros, I., Mitra, G. (eds): Annals of Operations Research, 99, Applied Mathematical Programming and Modeling IV (AP-MOD 98) J.C. Baltzer AG, Science Publishers, Basel, Switzerland (2000)
Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign, IL, and Cambridge University Press, Cambridge (2002)
Wolfram, S.: The Mathematica Book. (Fourth Edition) Wolfram Media, Champaign, IL, and Cambridge University Press, Cambridge (2003)
Wolfram Research: Mathematica (Current version: 5.1). Wolfram Research, Inc., Champaign, IL (2004) (See http://www.wolfram.com)
Zabinsky, Z.B.: Stochastic Adaptive Search for Global Optimization. Kluwer Academic Publishers, Boston/Dordrecht/London (2003)
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Pintér, J.D. (2005). Nonlinear Optimization in Modeling Environments. In: Jeyakumar, V., Rubinov, A. (eds) Continuous Optimization. Applied Optimization, vol 99. Springer, Boston, MA. https://doi.org/10.1007/0-387-26771-9_5
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DOI: https://doi.org/10.1007/0-387-26771-9_5
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