Semideterministic global optimization method: Application to a control problem of the Burgers equation

Journal of Optimization Theory and Applications

Volumn 135, Issue 3, 2007, Pages 549-561

  Ivorra, B ^a   Ramos, A M ^a   Mohammadi, B ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b Mathematics and Modeling Institute   (France)

Author keywords

Burgers equation; Genetic algorithm; Global optimization; Optimal control problem; Semideterministic algorithm

Indexed keywords

BOUNDARY VALUE PROBLEMS; GLOBAL OPTIMIZATION; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

BOUNDARY-VALUE PROBLEM; BURGER'S EQUATIONS; CONTROL PROBLEMS; GLOBAL OPTIMISATION; GLOBAL OPTIMIZATION ALGORITHM; GLOBAL OPTIMIZATION METHOD; OPTIMAL CONTROL PROBLEM; OPTIMIZATION PROBLEMS; POINTWISE CONTROL; SEMIDETERMINISTIC ALGORITHM;

GENETIC ALGORITHMS;

EID: 36148960894     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-007-9251-8     Document Type: Article

References (12)

1. Mohammadi, B., Saiac, J.H.: Pratique de la Simulation Numérique. Dunod, Paris (2002)
2. Attouch, H., Cominetti, R.: A dynamical approach to convex minimization coupling approximation with the steepest descent method. J. Differ. Equ. 128(2), 519-540 (1996)
3. Shivamoggi, B.K.: Theoretical Fluid Dynamics. Martinus Nijhoff Publishers, Dordrecht (1985)
4. Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)
5. Dumas, L., Herbert, V., Muyl, F.: Hybrid method for aerodynamic shape optimization in automotive industry. Comput. Fluids 33(5), 849-858 (2004)
6. Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large-scale optimization. Math. Program. 45, 503-528 (1989)
7. Ivorra, B. Semi-deterministic global optimization. PhD Thesis, Montpellier University, France (2006)
8. Debiane, L., Ivorra, B., Mohammadi, B., Nicoud, F., Ern, A., Poinsot, T., Pitsch, H.: A low-complexity global optimization algorithm for temperature and pollution control in flames with complex chemistry. Int. J. Comput. Fluid Dyn. 20(2), 93-98 (2006)
9. Ivorra, B., Mohammadi, B., Santiago, J.G., Hertzog, D.E.: Semi-deterministic and genetic algorithms for global optimization of microfluidic protein folding devices. Int. J. Numer. Methods Eng. 66(2), 319-333 (2006)
10. Ivorra, B., Mohammadi, B., Redont, P., Dumas, L., Durand, O.: Semi-deterministic vs. genetic algorithms for global optimization of multichannel optical filters. Int. J. Comput. Sci. Eng. 2(3), 170-178 (2006)
11. Broyden, C.G., Fletcher, R., Goldfarb, D., Shanno, D.F.: BFGS method. J. Inst. Math. Appl. 6, 76-90 (1970)
12. Ramos, A.M., Glowinski, R., Periaux, J.: Pointwise control of the Burgers equation and related Nash equilibrium problems: computational approach. J. Optim. Theory Appl. 112(3), 499-516 (2002)