## Main Article Content

## Abstract

We deal with the design of parallel algorithms by using variable partitioning techniques to solve nonlinear optimization problems. We propose an iterative solution method that is very efficient for separable functions, our scope being to discuss its performance for general functions. Experimental results on an illustrative example have suggested some useful modifications that, even though they improve the efficiency of our parallel method, leave some questions open for further investigation.

## Keywords

## Article Details

* * References

- Schnabel, R.B. A view of the limitations, opportunities, and challenges in parallel nonlinear optimization. Parallel Computing . 1995, 21(6), 875-905.
- Bertsekas, D.P. and Tsitsiklis, J.N. Parallel and Distributed Computation: Numerical Methods. Athena Scientific, Belmont-USA, 1997.
- Triki, C. and Grandinetti L. Computational grids to solve large scale optimization problems with uncertain data. International Journal of Computing 2002, 1(1), 20-26.
- Migdalas, A., Toraldo, G. and Kumar, V. Nonlinear optimization and parallel computing. Parallel Computing 2003, 29(4), 375-391.
- Beraldi, P., Grandinetti, L., Musmanno, R. and Triki, C. Parallel algorithms to solve two-stage stochastic linear programs with robustness constraints. Parallel Computing. 2000, 26(13-14), 1889-1908.
- D'Apuzzo, M. and Marino, M. Parallel computational issues of an interior point method for solving large bound-constrained quadratic programming problems. Parallel Computing 2003, 29(4), 467-483.
- Blomvall. J. A multistage stochastic programming algorithm suitable for parallel computing. Parallel Computing, 2003, 29(4), 431-445.
- Giraud, L., Haidar, A. and Pralet. S. Using multiple levels of parallelism to enhance the performance of domain decomposition solvers. Parallel Computing, 2010, 36(5-6), 285-296.
- Argello, F., Heras, D.B., Bo, M. and Lamas-Rodrguez, J. The split-and-merge method in general purpose computation on GPUs. Parallel Computing, 2012, 38(6-7), 277-288.
- Triki, C. Solving the flood propagation problem with Newton algorithm on parallel systems. SQU Journal for Science, 2012, 17(1), 147-156,
- Ferris, M.C. and Mangasarian, O.L. Parallel variable distribution. SIAM Journal on Optimization, 1994, 4, 815-832.
- Mangasarian, O.L. Parallel gradient distribution in unconstrained optimization. SIAM Journal on Optimization, 1995, 33, 1916-1925.
- Rotiroti, D., Triki, C. and Grandinetti, L. Combined MPI/OpenMP implementations for a stochastic programming solver. In Parallel Computing Advances and Current Issues (Edited by G. Joubert, A. Murli, F. Peters and M. Vanneschi), Imperial College Press, 2002.
- Zeng. D. Parallel iterative methods for nonlinear programming problems. Advanced Materials Research, 2010, 159,105-110.
- Li, W. A parallel multi-start search algorithm for dynamic traveling salesman problem. Lecture Notes in Computer Science, 2011, 6630, 65-75.
- Fletcher, R. Practical Methods of Optimization. Wiley, New York, 1987.
- Al-Baali, M. and Khalfan, H. An overview of some practical quasi-Newton methods for unconstrained optimization. SQU Journal for Science, 2007, 12(2), 199-209.
- Al-Baali, M. Solving Optimization Problems on Parallel Computers. Technical Report DMCS 1/95, UAE University, UAE, 1995
- Ruszczynski, A.P. Nonlinear Optimization. Princeton University Press, New Jersey, 2006
- Grama, A. and Kumar, V. Load balancing for parallel optimization techniques. Encyclopedia of Optimization, 2008, 1905-1911.
- Sinnen, O. Task Scheduling for Parallel Systems. Wiley-Interscience, New Jersey, 2007

#### References

Schnabel, R.B. A view of the limitations, opportunities, and challenges in parallel nonlinear optimization. Parallel Computing . 1995, 21(6), 875-905.

Bertsekas, D.P. and Tsitsiklis, J.N. Parallel and Distributed Computation: Numerical Methods. Athena Scientific, Belmont-USA, 1997.

Triki, C. and Grandinetti L. Computational grids to solve large scale optimization problems with uncertain data. International Journal of Computing 2002, 1(1), 20-26.

Migdalas, A., Toraldo, G. and Kumar, V. Nonlinear optimization and parallel computing. Parallel Computing 2003, 29(4), 375-391.

Beraldi, P., Grandinetti, L., Musmanno, R. and Triki, C. Parallel algorithms to solve two-stage stochastic linear programs with robustness constraints. Parallel Computing. 2000, 26(13-14), 1889-1908.

D'Apuzzo, M. and Marino, M. Parallel computational issues of an interior point method for solving large bound-constrained quadratic programming problems. Parallel Computing 2003, 29(4), 467-483.

Blomvall. J. A multistage stochastic programming algorithm suitable for parallel computing. Parallel Computing, 2003, 29(4), 431-445.

Giraud, L., Haidar, A. and Pralet. S. Using multiple levels of parallelism to enhance the performance of domain decomposition solvers. Parallel Computing, 2010, 36(5-6), 285-296.

Argello, F., Heras, D.B., Bo, M. and Lamas-Rodrguez, J. The split-and-merge method in general purpose computation on GPUs. Parallel Computing, 2012, 38(6-7), 277-288.

Triki, C. Solving the flood propagation problem with Newton algorithm on parallel systems. SQU Journal for Science, 2012, 17(1), 147-156,

Ferris, M.C. and Mangasarian, O.L. Parallel variable distribution. SIAM Journal on Optimization, 1994, 4, 815-832.

Mangasarian, O.L. Parallel gradient distribution in unconstrained optimization. SIAM Journal on Optimization, 1995, 33, 1916-1925.

Rotiroti, D., Triki, C. and Grandinetti, L. Combined MPI/OpenMP implementations for a stochastic programming solver. In Parallel Computing Advances and Current Issues (Edited by G. Joubert, A. Murli, F. Peters and M. Vanneschi), Imperial College Press, 2002.

Zeng. D. Parallel iterative methods for nonlinear programming problems. Advanced Materials Research, 2010, 159,105-110.

Li, W. A parallel multi-start search algorithm for dynamic traveling salesman problem. Lecture Notes in Computer Science, 2011, 6630, 65-75.

Fletcher, R. Practical Methods of Optimization. Wiley, New York, 1987.

Al-Baali, M. and Khalfan, H. An overview of some practical quasi-Newton methods for unconstrained optimization. SQU Journal for Science, 2007, 12(2), 199-209.

Al-Baali, M. Solving Optimization Problems on Parallel Computers. Technical Report DMCS 1/95, UAE University, UAE, 1995

Ruszczynski, A.P. Nonlinear Optimization. Princeton University Press, New Jersey, 2006

Grama, A. and Kumar, V. Load balancing for parallel optimization techniques. Encyclopedia of Optimization, 2008, 1905-1911.

Sinnen, O. Task Scheduling for Parallel Systems. Wiley-Interscience, New Jersey, 2007