GlobSol: History, Composition, and Advice on Use

The GlobSol software package combines various ideas from interval analysis, automatic differentiation, and constraint propagation to provide verified solutions to unconstrained and constrained global optimization problems. After briefly reviewing some of these techniques and GlobSol’s development history, we provide the first overall description of GlobSol’s algorithm. Giving advice on use, we point out strengths and weaknesses in GlobSol’s approaches. Through examples, we show how to configure and use GlobSol.

[1]  Pascal Van Hentenryck,et al.  Numerica: A Modeling Language for Global Optimization , 1997, IJCAI.

[2]  Louis B. Rall,et al.  Automatic Differentiation: Techniques and Applications , 1981, Lecture Notes in Computer Science.

[3]  R. B. Kearfott.  Rigorous Global Search: Continuous Problems , 1996 .

[4]  Mark A. Stadtherr,et al.  NONLINEAR PARAMETER ESTIMATION USING INTERVAL ANALYSIS , 1998 .

[5]  W. Lodwick,et al.  An improved unconstrained global optimization algorithm , 1996 .

[6]  R. Baker Kearfott,et al.  On proving existence of feasible points in equality constrained optimization problems , 1998, Math. Program..

[7]  Chenyi Hu,et al.  Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library , 1994, TOMS.

[8]  R. Baker Kearfott,et al.  Algorithm 681: INTBIS, a portable interval Newton/bisection package , 1990, TOMS.

[9]  A. Griewank,et al.  Automatic differentiation of algorithms : theory, implementation, and application , 1994 .

[10]  Martin Berz,et al.  Computational differentiation : techniques, applications, and tools , 1996 .

[11]  R. Baker Kearfott.  Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Systems , 1997, SIAM J. Sci. Comput..

[12]  R. B. Kearfott,et al.  Abstract generalized bisection and a cost bound , 1987 .

[13]  George F. Corliss,et al.  Rigorous Global Search: Industrial Applications , 1998, SCAN.

[14]  R. Baker Kearfott,et al.  An interval branch and bound algorithm for bound constrained optimization problems , 1992, J. Glob. Optim..

[15]  Carol Ann Schnepper,et al.  Large-grained parallelism in equation-based flowsheeting using interval Newton/generalized bisection techniques , 1992 .

[16]  Andreas Griewank,et al.  Automatic Differentiation of Algorithms: From Simulation to Optimization , 2000, Springer New York.

[17]  G. William Walster,et al.  Symbolic Preconditioning with Taylor Models: Some Examples , 2002, Reliab. Comput..

[18]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[19]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[20]  R. Baker Kearfott,et al.  Algorithm 763: INTERVAL_ARITHMETIC: a Fortran 90 module for an interval data type , 1996, TOMS.

[21]  A. Neumaier.  Interval methods for systems of equations , 1990 .

[22]  Andreas Griewank,et al.  Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++ , 1996, TOMS.

[23]  G. William Walster,et al.  On stopping criteria in verified nonlinear systems or optimization algorithms , 2000, TOMS.

[24]  Tibor Csendes,et al.  On the selection of subdivision directions in interval branch-and-bound methods for global optimization , 1995, J. Glob. Optim..

[25]  Ralph Baker Kearfott,et al.  An Iterative Method for Finding Approximate Feasible Points , 2000 .

[26]  A. Morgan.  Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems , 1987 .

[27]  Philip E. Gill,et al.  Practical optimization , 1981 .

[28]  C. Lemaréchal.  Nondifferentiable optimization , 1989 .