Nonlinear optimization with GAMS /LGO

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.

[1]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

[2]  János D. Pintér,et al.  LGO — A Program System for Continuous and Lipschitz Global Optimization , 1997 .

[3]  J. Pintér,et al.  GAMS/LGO Nonlinear Solver Suite: Key Features, Usage, and Numerical Performance , 2003 .

[4]  R. Faure,et al.  Introduction to operations research , 1968 .

[5]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[6]  Abdellah Salhi,et al.  Global Optimization: Deterministic Approaches (2nd Edition) , 1994 .

[7]  N. Sahinidis,et al.  Convexification and Global Optimization in Continuous And , 2002 .

[8]  Pablo Moscato,et al.  Handbook of Applied Optimization , 2000 .

[9]  Michael C. Ferris,et al.  MATLAB and GAMS: Interfacing Optimization and Visualization Software , 1999 .

[10]  M. Bartholomew-Biggs Nonlinear Optimization with Financial Applications , 2005 .

[11]  J. D. Pinter,et al.  Configuration Analysis and Design by Using Optimization Tools in Mathematica , 2006 .

[12]  G. Taylor Introduction to Environmental Management , 1994 .

[13]  János D. Pintér Globally Optimized Spherical Point Arrangements: Model Variants and Illustrative Results , 2001, Ann. Oper. Res..

[14]  János D. Pintér,et al.  A Global Optimization Approach to Laser Design , 2003 .

[15]  Klaus Schittkowski,et al.  Numerical Data Fitting in Dynamical Systems , 2002 .

[16]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[17]  János D. Pintér,et al.  Finding elliptic Fekete points sets: two numerical solution approaches , 2001 .

[18]  Michael R. Bussieck,et al.  Quality Assurance and Global Optimization , 2002, COCOS.

[19]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[20]  Didier Henrion Global Optimization Toolbox for Maple , 2006 .

[21]  J. Pintér Global optimization : scientific and engineering case studies , 2006 .

[22]  John C. Plummer,et al.  A Multistart Scatter Search Heuristic for Smooth NLP and MINLP Problems , 2005 .

[23]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[24]  Neil Gershenfeld,et al.  The nature of mathematical modeling , 1998 .

[25]  Nicholas I. M. Gould,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[26]  Tamás Vinkó,et al.  A comparison of complete global optimization solvers , 2005, Math. Program..

[27]  M. J. D. Powell,et al.  UOBYQA: unconstrained optimization by quadratic approximation , 2002, Math. Program..

[28]  Robert L. Smith,et al.  Pure adaptive search in global optimization , 1992, Math. Program..

[29]  A. Ruszczynski,et al.  Nonlinear Optimization , 2006 .

[30]  Zelda B. Zabinsky,et al.  Stochastic Adaptive Search for Global Optimization , 2003 .

[31]  Rutherford Aris,et al.  Mathematical modeling : a chemical engineer's perspective , 1999 .

[32]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[33]  Etienne Huens,et al.  Algorithms for Solving Non-Linear Constrained and Optimization Problems: The State of The Art , 2001 .

[34]  János Pintér Globally optimized calibration of environmental models , 1990 .

[35]  Michael T. Heath,et al.  Scientific Computing , 2018 .

[36]  E. Kreyszig,et al.  Advanced Engineering Mathematics. , 1974 .

[37]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2005, SIAM Rev..

[38]  Stuart Smith,et al.  Solving Large Sparse Nonlinear Programs Using GRG , 1992, INFORMS J. Comput..

[39]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[40]  Hans D. Mittelmann,et al.  A server for automated performance analysis of benchmarking data , 2006, Optim. Methods Softw..

[41]  Stephen Wolfram,et al.  The Mathematica book (4th edition) , 1999 .

[42]  János D. Pintér,et al.  Nonlinear Optimization in Modeling Environments , 2005 .

[43]  J. Pintér Nonlinear Optimization in Modeling Environments Software Implementations for Compilers , Spreadsheets , Modeling Languages , and Integrated Computing Systems , 2005 .

[44]  Sven Leyffer,et al.  User manual for filterSQP , 1998 .

[45]  Klaus Schittkowski,et al.  Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software , 2002 .

[46]  Nicholas I. M. Gould,et al.  GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization , 2003, TOMS.

[47]  Christodoulos A. Floudas,et al.  Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications) , 2005 .

[48]  Srdjan Stojanovic Computational Financial Mathematics using MATHEMATICA , 2003 .

[49]  A. Neumaier Acta Numerica 2004: Complete search in continuous global optimization and constraint satisfaction , 2004 .

[50]  W. R. Howard The Nature of Mathematical Modeling , 2006 .

[51]  Sven Leyffer,et al.  Nonlinear programming without a penalty function , 2002, Math. Program..

[52]  Didier Henrion A review of the Global Optimization Toolbox for Maple , 2006 .

[53]  D. Dörner The logic of failure. , 1990, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[54]  D. Himmelblau,et al.  Optimization of Chemical Processes , 1987 .

[55]  N. T. Hoai-Phuong,et al.  Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set , 2006 .

[56]  János D. Pintér,et al.  Solving circle packing problems by global optimization: Numerical results and industrial applications , 2008, Eur. J. Oper. Res..

[57]  János D. Pintér,et al.  Globally optimized calibration of nonlinear models: Techniques, software, and applications , 2003, Optim. Methods Softw..

[58]  János D. Pintér,et al.  MathOptimizer Professional: Key Features and Illustrative Applications , 2006 .

[59]  Y. D. Sergeyev,et al.  Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications) , 2000 .

[60]  Zelda B. Zabinsky,et al.  A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems , 2005, J. Glob. Optim..

[61]  Willi-Hans Steeb,et al.  The Nonlinear Workbook , 2005 .

[62]  Margaret H. Wright,et al.  Direct search methods: Once scorned, now respectable , 1996 .

[63]  Zelda B. Zabinsky,et al.  Comparative Assessment of Algorithms and Software for Global Optimization , 2005, J. Glob. Optim..

[64]  G. McCormick,et al.  Selected applications of nonlinear programming , 1968 .

[65]  János D. Pintér,et al.  Global Optimization: Software, Test Problems, and Applications , 2002 .

[66]  J D Pinter,et al.  Global Optimization in Action—Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications , 2010 .

[67]  R. Vanderbei LOQO user's manual — version 3.10 , 1999 .

[68]  János D. Pintér,et al.  Introduction to Applied Optimization , 2007, Eur. J. Oper. Res..

[69]  A. Neumaier Complete search in continuous global optimization and constraint satisfaction , 2004, Acta Numerica.

[70]  János D. Pintér,et al.  Global Optimization Toolbox for Maple: an introduction with illustrative applications , 2006, Optim. Methods Softw..

[71]  J. Pintér,et al.  Nonlinear Optimization in Mathematica with MathOptimizer Professional , 2005 .

[72]  Nikolaos V. Sahinidis,et al.  Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming , 2002 .

[73]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[74]  Panos Y. Papalambros,et al.  Principles of Optimal Design: Author Index , 2000 .

[75]  János D. Pintér,et al.  An Optimization-Based Approach to the Multiple Static Delivery Technique in Radiation Therapy , 2003, Ann. Oper. Res..