## GLOPT - A Program for Constrained Global Optimization (1996)

Venue: | Developments in Global Optimization |

Citations: | 15 - 7 self |

### BibTeX

@INPROCEEDINGS{Dallwig96glopt-,

author = {S. Dallwig and A. Neumaier and H. Schichl},

title = {GLOPT - A Program for Constrained Global Optimization},

booktitle = {Developments in Global Optimization},

year = {1996},

pages = {pp.},

publisher = {Kluwer}

}

### Years of Citing Articles

### OpenURL

### Abstract

. GLOPT is a Fortran77 program for global minimization of a blockseparable 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. GLOPT 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. In 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 inf...

### Citations

1167 | Handbook of Genetic Algorithms
- Davis
- 1991
(Show Context)
Citation Context ...r (Dixon & Szeg o [8], Mockus [29], T orn & Zilinskas [41]). More recently, a number of other techniques like simulated annealing (Kirkpatrick et al. [24]) and genetic algorithmss(Holland [13], Davis =-=[6]-=-) have been developed, using analogies to physics and biology to approach the global optimum. All these techniques have in common the fact that they tend to find better and better local minima, but --... |

529 |
Methods and Applications of Interval Analysis
- Moore
- 1979
(Show Context)
Citation Context ...can be made to work also in the continuous case, where the variables may take a continuous range of values (Pardalos & Rosen [36], Horst & Pardalos [14]). Using techniques of interval analysis (Moore =-=[30]-=-, Neumaier [33]), it is possible to find lower bounds for the objective over extended boxes in configuration space, and the branching technique can be adapted from the combinatorial situation by split... |

506 |
Interval Methods for Systems of Equations
- Neumaier
- 1990
(Show Context)
Citation Context ...work also in the continuous case, where the variables may take a continuous range of values (Pardalos & Rosen [36], Horst & Pardalos [14]). Using techniques of interval analysis (Moore [30], Neumaier =-=[33]-=-), it is possible to find lower bounds for the objective over extended boxes in configuration space, and the branching technique can be adapted from the combinatorial situation by splitting such boxes... |

465 |
Global optimization Using Interval Analysis
- HANSEN
- 1001
(Show Context)
Citation Context ...oxes. Indeed, interval branch and bound methods have been successfully used on the related problem of finding all solutions of nonlinear systems, and also in unconstrained global optimization (Hansen =-=[12]-=-). However, many practical problems involve general linear or nonlinear constraints, and until recently there were no programs that can solve such problems except in very small dimensions or special s... |

213 |
Optimization by simulated annealing, Science 220
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ...al techniques, this approach can be refined further (Dixon & Szeg o [8], Mockus [29], T orn & Zilinskas [41]). More recently, a number of other techniques like simulated annealing (Kirkpatrick et al. =-=[24]-=-) and genetic algorithmss(Holland [13], Davis [6]) have been developed, using analogies to physics and biology to approach the global optimum. All these techniques have in common the fact that they te... |

208 |
Global Optimization
- Torn, Zilinskas
- 1989
(Show Context)
Citation Context ...e enough to the global minimizer so that local optimization reaches it. Using suitable statistical techniques, this approach can be refined further (Dixon & Szeg o [8], Mockus [29], T orn & Zilinskas =-=[41]-=-). More recently, a number of other techniques like simulated annealing (Kirkpatrick et al. [24]) and genetic algorithmss(Holland [13], Davis [6]) have been developed, using analogies to physics and b... |

169 | Older: Applying Interval Arithmetic to Real, Integer and Bolean Constraints
- Benhamou, W
- 1995
(Show Context)
Citation Context ...hematically equivalent but computationally slower forms of the above reduction process have been used in the Unicalc branch and bound zero finder [1] under the name of subdefinite programming, and in =-=[2, 4, 11, 15, 16, 17, 26, 42]-=- under the name of interval constraint propagation, used in a branch and bound context (for zeros of nonlinear systems) by van Hentenryck et al. [43]. 6. Examples and test results We first give a simp... |

121 |
Pardalos. A collection of test problems for constrained global optimization algorithms
- Floudas, M
- 1990
(Show Context)
Citation Context ... a check for its usefulness and user friendliness, and simultaneously as a basis for testing various versions of our algorithm, we coded in NOP over 60 test problems from three well-known collections =-=[10, 19, 44]-=- of global optimization test problems. While NOP is already in a very useful stage, it still has some inefficiencies, and we are experimenting with some modifications. We developed a NOP reader that t... |

103 |
Constraint reasoning based on interval arithmetic: The tolerance propagation approach
- Hyvönen
- 1992
(Show Context)
Citation Context ...hematically equivalent but computationally slower forms of the above reduction process have been used in the Unicalc branch and bound zero finder [1] under the name of subdefinite programming, and in =-=[2, 4, 11, 15, 16, 17, 26, 42]-=- under the name of interval constraint propagation, used in a branch and bound context (for zeros of nonlinear systems) by van Hentenryck et al. [43]. 6. Examples and test results We first give a simp... |

101 | Solving Polynomial Systems Using a Branch and Prune Approach
- Hentenryck, McAllester, et al.
- 1997
(Show Context)
Citation Context ...nite programming, and in [2, 4, 11, 15, 16, 17, 26, 42] under the name of interval constraint propagation, used in a branch and bound context (for zeros of nonlinear systems) by van Hentenryck et al. =-=[43]-=-. 6. Examples and test results We first give a simple illustration for the working of feas and reduce. The NOP file for minimizing the well-known Rosenbrock function f(x) = (10x 2 1 \Gamma 10x 2 ) 2 +... |

83 |
Genetic Algorithms and the Optimal Allocation of Trials
- Holland
- 1973
(Show Context)
Citation Context ...fined further (Dixon & Szeg o [8], Mockus [29], T orn & Zilinskas [41]). More recently, a number of other techniques like simulated annealing (Kirkpatrick et al. [24]) and genetic algorithmss(Holland =-=[13]-=-, Davis [6]) have been developed, using analogies to physics and biology to approach the global optimum. All these techniques have in common the fact that they tend to find better and better local min... |

50 | Preconditioners for the interval Gauss-Seidel method
- Kearfott
- 1990
(Show Context)
Citation Context ...x ] f Figure 3. Shrinking a box by reduce version of the generalized Gauss-Seidel method for linear interval equations, introduced in Neumaier [32], p.180, and later used by Kearfottsand his students =-=[21, 22, 40]-=-. For the mathematical formulation we need the inner addition [a; a] ffi + [b; b] := [a + b; a + b] of intervals. This differs from the standard interval operations, where [a; a] + [b; b] := [a + b; a... |

47 | Subdivision Direction Selection in Interval Methods for Global Optimization
- Csendes, Ratz
- 1997
(Show Context)
Citation Context ...entation is further enhanced by a number of smaller features improving performance, such as details of box selection and branching strategy. Possible techniques for doing this are discussed, e.g., in =-=[3, 5, 18, 23, 37, 38]-=-, mainly for the bound constraint case. More general constraints may need deviations from these principles. Since our current implementaion is preliminary and it is unclear to which extend these will ... |

41 |
Bayesian Approach to Global Optimization
- Mockus
- 1989
(Show Context)
Citation Context ...that one of them is close enough to the global minimizer so that local optimization reaches it. Using suitable statistical techniques, this approach can be refined further (Dixon & Szeg o [8], Mockus =-=[29]-=-, T orn & Zilinskas [41]). More recently, a number of other techniques like simulated annealing (Kirkpatrick et al. [24]) and genetic algorithmss(Holland [13], Davis [6]) have been developed, using an... |

41 |
Constrained Global Optimization: Algorithms and Applications
- Pardalos, Rosen
- 1987
(Show Context)
Citation Context ...sulting tree of subproblems must be generated and processed. The same idea can be made to work also in the continuous case, where the variables may take a continuous range of values (Pardalos & Rosen =-=[36]-=-, Horst & Pardalos [14]). Using techniques of interval analysis (Moore [30], Neumaier [33]), it is possible to find lower bounds for the objective over extended boxes in configuration space, and the b... |

34 |
The Tunneling Algorithm for the Global Minimization of Functions
- Levy, Montalvo
- 1985
(Show Context)
Citation Context ...s does not work, and in particular always when there are intrinsic equality constraints, the more expensive tunneling strategy is tried. The idea is taken from the tunneling method of Levy & Montalvo =-=[25]-=- for unconstrained optimization, although the technique used there is heuristic only, and completely different. tunnel attempts to find a point better than the currently best point by a procedure that... |

34 |
Global minimum potential energy conformations of small molecules
- Maranas, Floudas
- 1994
(Show Context)
Citation Context ...obal Optimization 3 ly, general purpose constrained global optimization programs that do not restrict the form of the constraints are becoming available (Epperly [9], Kearfott [23], Maranas & Floudas =-=[27, 28]-=-, Schnepper & Stadtherr [39]). GLOPT is a long-term project aiming at the development of software for fast and reliable constrained optimization by exploiting the special structure of the problems so ... |

30 | Floudas. Finding all solutions of nonlinearly constrained systems of equations
- Maranas, A
- 1995
(Show Context)
Citation Context ...obal Optimization 3 ly, general purpose constrained global optimization programs that do not restrict the form of the constraints are becoming available (Epperly [9], Kearfott [23], Maranas & Floudas =-=[27, 28]-=-, Schnepper & Stadtherr [39]). GLOPT is a long-term project aiming at the development of software for fast and reliable constrained optimization by exploiting the special structure of the problems so ... |

30 | T.: On the selection of subdivision directions in interval branch-and-bound methods for global optimization
- Ratz, Csendes
- 1995
(Show Context)
Citation Context ...entation is further enhanced by a number of smaller features improving performance, such as details of box selection and branching strategy. Possible techniques for doing this are discussed, e.g., in =-=[3, 5, 18, 23, 37, 38]-=-, mainly for the bound constraint case. More general constraints may need deviations from these principles. Since our current implementaion is preliminary and it is unclear to which extend these will ... |

27 |
Towards Global Optimization
- Dixon, Szego
- 1975
(Show Context)
Citation Context ...nts, hoping that one of them is close enough to the global minimizer so that local optimization reaches it. Using suitable statistical techniques, this approach can be refined further (Dixon & Szeg o =-=[8]-=-, Mockus [29], T orn & Zilinskas [41]). More recently, a number of other techniques like simulated annealing (Kirkpatrick et al. [24]) and genetic algorithmss(Holland [13], Davis [6]) have been develo... |

25 | A review of techniques in the verified solution of constrained global optimization problems
- Kearfott
- 1996
(Show Context)
Citation Context ...o v.; p.2 Constrained Global Optimization 3 ly, general purpose constrained global optimization programs that do not restrict the form of the constraints are becoming available (Epperly [9], Kearfott =-=[23]-=-, Maranas & Floudas [27, 28], Schnepper & Stadtherr [39]). GLOPT is a long-term project aiming at the development of software for fast and reliable constrained optimization by exploiting the special s... |

22 |
A Global Minimization Method: the Multi-Dimensional Case
- Jansson, Knueppel
- 1992
(Show Context)
Citation Context ...cursively into subproblems that are either eliminated or reduced in their size, making extensive use of the block separable structure of the optimization problem. As in a method by Jansson & Kn uppel =-=[19]-=- for bound constrained global optimization, no derivative information is used in GLOPT. This information is used in three separate tasks called feas, tunnelsand reduce. They are novel improvements of ... |

20 | Decomposition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems. Computing 47(2
- Kearfott
- 1991
(Show Context)
Citation Context ...x ] f Figure 3. Shrinking a box by reduce version of the generalized Gauss-Seidel method for linear interval equations, introduced in Neumaier [32], p.180, and later used by Kearfottsand his students =-=[21, 22, 40]-=-. For the mathematical formulation we need the inner addition [a; a] ffi + [b; b] := [a + b; a + b] of intervals. This differs from the standard interval operations, where [a; a] + [b; b] := [a + b; a... |

18 |
Pardalos (Eds.), Handbook of Global Optimization
- Horst, M
- 1995
(Show Context)
Citation Context ...lems must be generated and processed. The same idea can be made to work also in the continuous case, where the variables may take a continuous range of values (Pardalos & Rosen [36], Horst & Pardalos =-=[14]-=-). Using techniques of interval analysis (Moore [30], Neumaier [33]), it is possible to find lower bounds for the objective over extended boxes in configuration space, and the branching technique can ... |

16 |
Test Results for a Global Optimization Algorithm, Numerical Optimization
- WALSTER, HANSEN, et al.
- 1984
(Show Context)
Citation Context ... a check for its usefulness and user friendliness, and simultaneously as a basis for testing various versions of our algorithm, we coded in NOP over 60 test problems from three well-known collections =-=[10, 19, 44]-=- of global optimization test problems. While NOP is already in a very useful stage, it still has some inefficiencies, and we are experimenting with some modifications. We developed a NOP reader that t... |

15 | a novel approach to solving systems of algebraic equations
- Babichev, Kadyrova, et al.
- 1993
(Show Context)
Citation Context ... does not lead to a strict improvement of the box. Mathematically equivalent but computationally slower forms of the above reduction process have been used in the Unicalc branch and bound zero finder =-=[1]-=- under the name of subdefinite programming, and in [2, 4, 11, 15, 16, 17, 26, 42] under the name of interval constraint propagation, used in a branch and bound context (for zeros of nonlinear systems)... |

13 |
Application of a parallel interval Newton~generalized bisection algorithm to equation-based chemical process flowsheeting. Interval Computations 4
- Schnepper, Stadther
- 1993
(Show Context)
Citation Context ...purpose constrained global optimization programs that do not restrict the form of the constraints are becoming available (Epperly [9], Kearfott [23], Maranas & Floudas [27, 28], Schnepper & Stadtherr =-=[39]-=-). GLOPT is a long-term project aiming at the development of software for fast and reliable constrained optimization by exploiting the special structure of the problems so that higherdimensional probl... |

10 |
Algorithm 573 NL2SOL: an adaptive nonlinear least-square algorithm [E4
- Dennis, Gay, et al.
(Show Context)
Citation Context ... (8). In our GLOPT implementation, we solve the bound constrained tunneling least squares problem using the PORT routine nf2b, an implementation by David Gay based on the NL2SOL code of Dennis et al. =-=[7]-=-. 5. Box reduction The routine reduce attempts to shrink a box by elimination of a part of it that can be shown not to contain a point better than the best point found already. At the moment, this is ... |

9 | Global Optimization of Nonconvex Nonlinear Programs Using Parallel Branch and Bound
- Epperly
- 1995
(Show Context)
Citation Context ...1996; 12:46; no v.; p.2 Constrained Global Optimization 3 ly, general purpose constrained global optimization programs that do not restrict the form of the constraints are becoming available (Epperly =-=[9]-=-, Kearfott [23], Maranas & Floudas [27, 28], Schnepper & Stadtherr [39]). GLOPT is a long-term project aiming at the development of software for fast and reliable constrained optimization by exploitin... |

9 | Second-order sufficient optimality conditions for local and global nonlinear programming
- Neumaier
- 1996
(Show Context)
Citation Context ... problems. We are currently working on an implementation of underestimation techniques and second order techniques (related to gloptk.tex; 12/04/1996; 12:46; no v.; p.15 16 S. DALLWIG et al. Neumaier =-=[34]-=-) that eliminate the problem of not using simultaneous information, thus overcoming the main inefficiency. Acknowledgment Part of this work has been done with support by the European External Research... |

8 | Solving large systems of nonlinear constraints with application to data modeling
- Hager
- 1993
(Show Context)
Citation Context ...hematically equivalent but computationally slower forms of the above reduction process have been used in the Unicalc branch and bound zero finder [1] under the name of subdefinite programming, and in =-=[2, 4, 11, 15, 16, 17, 26, 42]-=- under the name of interval constraint propagation, used in a branch and bound context (for zeros of nonlinear systems) by van Hentenryck et al. [43]. 6. Examples and test results We first give a simp... |

8 |
The enclosure of solutions of parameter-dependent systems of equations
- Neumaier
- 1988
(Show Context)
Citation Context ...4/1996; 12:46; no v.; p.9 10 S. DALLWIG et al. 2 [x ] 1 [x ] f Figure 3. Shrinking a box by reduce version of the generalized Gauss-Seidel method for linear interval equations, introduced in Neumaier =-=[32]-=-, p.180, and later used by Kearfottsand his students [21, 22, 40]. For the mathematical formulation we need the inner addition [a; a] ffi + [b; b] := [a + b; a + b] of intervals. This differs from the... |

6 | Interval computations on the spreadsheet
- Hyvönen, Pascale
- 1996
(Show Context)
Citation Context |

5 | A branch and bound algorithm for bound constrained optimization problems without derivatives - Jansson, Knuppel - 1995 |

5 | On Branching Rules in Second-Order Branch-and-Bound Methods for Global Optimization
- Ratz
- 1996
(Show Context)
Citation Context ...entation is further enhanced by a number of smaller features improving performance, such as details of box selection and branching strategy. Possible techniques for doing this are discussed, e.g., in =-=[3, 5, 18, 23, 37, 38]-=-, mainly for the bound constraint case. More general constraints may need deviations from these principles. Since our current implementaion is preliminary and it is unclear to which extend these will ... |

4 |
On self-validating methods for optimization problems. pp. 381–438 in: Topics in validated computation
- Jansson
- 1994
(Show Context)
Citation Context |

4 |
Constraint propagation, relational arithmetic in ai systems and mathematical programs
- Lodwick
- 1989
(Show Context)
Citation Context |

3 |
Intermediate Expression Preconditioning and Verification for Rigorous Solution of Nonlinear Systems
- Shi
- 1995
(Show Context)
Citation Context .... The best function value gloptk.tex; 12/04/1996; 12:46; no v.; p.7 8 S. DALLWIG et al. 1 2 3 4 5 6 7 0 20 40 60 80 100 120 140 Figure 2. Finding better points by tunnel allows us to reduce [x 2 ] to =-=[10; 40]-=-, and (5) becomes min ((x 1 \Gamma 1) 2 (x 1 \Gamma 4)(x 1 \Gamma 6) + 40 \Gamma x 2 ) 2 s:t: x 1 2 [2:5; 6:5]; x 2 2 [10; 40]: (6) A local optimization, if successful, might find any point on the por... |

2 |
A Compact Input Format for Nonlinear Optimization Problems
- NOP
- 1997
(Show Context)
Citation Context ...e vector-valued function F resulting from transforming (1) and (2) to the form (3) is retained. For processing with GLOPT, constrained optimization problems are coded in the input format NOP (Neumaier=-=[35]-=-) that explicitly displays gloptk.tex; 12/04/1996; 12:46; no v.; p.3 4 S. DALLWIG et al. p reduce each half p store nonempty boxes p bisect stack empty? # of boxes in branch exceeded? feas tunnel redu... |

1 |
New results on verified global optimization, submitted
- Berner
- 1995
(Show Context)
Citation Context |

1 |
Emden, Adding interval constraints to the Moore-- Skelboe global optimization algorithm
- Chen, van
- 1995
(Show Context)
Citation Context |

1 |
Global consistency in interval constraint satisfaction
- Hyvonen
- 1991
(Show Context)
Citation Context |

1 |
Integer Programming, Chapter VI (pp. 447527
- Nemhauser, Wolsey
- 1989
(Show Context)
Citation Context ...and take a few values only, these techniques have the same potential and draw-backs. However, for combinatorial problems there is a methodology, called branch and bound (see, e.g., Nemhauser & Wolsey =-=[31]-=-) that permits a systematic exploration of the full configuration space of allowed combinations of variables, and yet avoids in many cases the exponential amount of work that a naive exhaustive search... |