GLOPT is a Fortran 77 program for global minimization of a block-separable objective function subject to bound constraints and block-separable constraints. It finds a nearly globally optimal point that is near a true local minimizer. Unless there are several local minimizers that are nearly global, we thus find a good approximation to the global minimizer. \parGLOPT uses a branch and bound technique to split the problem recursively into subproblems that are either eliminated or reduced in their size. This is done by an extensive use of the block separable structure of the optimization problem. \parIn this paper we discuss a new reduction technique for boxes and new ways for generating feasible points of constrained nonlinear programs. These are implemented as the first stage of our GLOPT project. The current implementation of GLOPT uses neither derivatives nor simultaneous information about several constraints. Numerical results are already encouraging. Work on an extension using curvature information and quadratic programming techniques is in progress.

References in zbMATH (referenced in 19 articles , 1 standard article )

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  1. Domes, Ferenc; Neumaier, Arnold: Constraint propagation on quadratic constraints (2010)
  2. Rump, Siegfried M.; Sekigawa, Hiroshi: The ratio between the Toeplitz and the unstructured condition number (2010)
  3. Li, D.; Sun, X.L.; Wang, J.; McKinnon, K.I.M.: Convergent Lagrangian and domain cut method for nonlinear knapsack problems (2009)
  4. Pedamallu, Chandra Sekhar; Özdamar, Linet; Csendes, Tibor; Vinkó, Tamás: Efficient interval partitioning for constrained global optimization (2008)
  5. Addis, Bernardetta; Locatelli, Marco: A new class of test functions for global optimization (2007)
  6. Neumaier, Arnold; Pownuk, Andrzej: Linear systems with large uncertainties, with applications to truss structures (2007)
  7. Pintér, János D.: Nonlinear optimization with GAMS /LGO (2007)
  8. Ali, M.Montaz; Khompatraporn, Charoenchai; Zabinsky, Zelda B.: A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems (2005)
  9. Bagirov, Adil M.; Rubinov, Alexander M.; Zhang, Jiapu: Local optimization method with global multidimensional search (2005)
  10. Jaulin, Luc; Henrion, Didier: Contracting optimally an interval matrix without loosing any positive semi-definite matrix is a tractable problem (2005)
  11. Kallrath, Josef: Solving planning and design problems in the process industry using mixed integer and global optimization (2005)
  12. Khompatraporn, Charoenchai; Pintér, János D.; Zabinsky, Zelda B.: Comparative assessment of algorithms and software for global optimization (2005)
  13. Lebbah, Yahia; Michel, Claude; Rueher, Michel: A rigorous global filtering algorithm for quadratic constraints (2005)
  14. Linderoth, Jeff: A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs (2005)
  15. Neumaier, Arnold; Shcherbina, Oleg; Huyer, Waltraud; Vinkó, Tamás: A comparison of complete global optimization solvers (2005)
  16. Nowak, Ivo: Lagrangian decomposition of block-separable mixed-integer all-quadratic programs (2005)
  17. Schichl, Hermann; Neumaier, Arnold: Interval analysis on directed acyclic graphs for global optimization (2005)
  18. Schichl, H.; Dallwig, S.; Neumaier, A.: The NOP-2 modeling language for nonlinear programming (2001)
  19. Dallwig, S.; Neumaier, A.; Schichl, H.: GLOPT - a program for constrained global optimization (1997)