A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

Armaou, A. and Christofides P. D. (2002). Dynamic optimization of dissipative PDE systems using nonlinear order reduction, Chemical Engineering Science 57: 5083-5114.10.1016/S0009-2509(02)00419-0Search in Google Scholar

Aschemanna, H., Kostinb, G. V., Rauha, A. and Saurinb, V. V. (2010). Approaches to control design and optimization in heat transfer problems, International Journal of Computer and Systems Sciences 49(3): 380-391.10.1134/S106423071003007XSearch in Google Scholar

Audet, C. and Dennis, J. E. (2004). A pattern search filter method for nonlinear programming without derivatives, SIAM Journal on Optimization 14(4): 980-1010.10.1137/S105262340138983XSearch in Google Scholar

Bellavia, S., Macconi, M. and Morini, B. (2004). STRSCNE: A scaled trust-region solver for constrained nonlinear equations, Computational Optimization and Applications 28(1): 31-50.10.1023/B:COAP.0000018878.95983.4eSearch in Google Scholar

Betts, J. T. (2010). Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd Edn., Society for Industrial and Applied Mathematics, Philadelphia, PA.Search in Google Scholar

Biegler, L. T. (2010). Nonlinear Programming. Concepts, Algorithms, and Applications to Chemical Processes, SIAM, Philadelphia, PA.10.1137/1.9780898719383Search in Google Scholar

Burger, J. and Pogu, M. (1991). Functional and numerical solution of a control problem originating from heat transfer, Journal of Optimization Theory and Applications 68(1): 49-73.10.1007/BF00939935Search in Google Scholar

Broyden, C. G. (1970). The convergence of a class of double-rank minimization algorithms, Journal of the Institute of Mathematics and Its Applications 6: 76-90.10.1093/imamat/6.1.76Search in Google Scholar

Butkovskiy, A. G. (1969). Distributed Control Systems, 1st Edn., Elsevier, New York, NY.Search in Google Scholar

Byrd, R. H., Curtis, F. E. and Nocedal, J. (2010). Infeasibility detection and SQPmethods for nonlinear optimization, SIAM Journal on Optimization 20(5): 2281-2299.10.1137/080738222Search in Google Scholar

Chin, C. M. and Fletcher, R. (2003). On the global convergence of an SLP-filter algorithm that takes EQP steps, Mathematical Programming 96(1): 161-177.10.1007/s10107-003-0378-6Search in Google Scholar

Chin, C. M., Rashid, A. H. A. and Nor, K. M. (2007). Global and local convergence of a filter line search method for non-linear programming, Optimization Methods and Software 22(3): 365-390.10.1080/10556780600565489Search in Google Scholar

Christofides, P. D. (2001). Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes, Birkhauser, Boston, MA.10.1007/978-1-4612-0185-4Search in Google Scholar

Conn, A. R., Gould, N. I. and Toint, P. L. (2000). Trust-Region Methods, MPS-SIAM Series on Optimization, SIAM, Philadelphia, PA.10.1137/1.9780898719857Search in Google Scholar

Demetriou, M. A. and Kazantzis, N. (2004). A new actuator activation policy for performance enhancement of controlled diffusion processes, Automatica 40(3): 415-421.10.1016/j.automatica.2003.10.023Search in Google Scholar

El-Farra, N. E., Armaou, A. and Christofides, P. D. (2003). Analysis and control of parabolic PDE systems with input constraints, Automatica 39(3): 715-725.10.1016/S0005-1098(02)00304-7Search in Google Scholar

Fattorini, H. O. (1999). Infinite Dimensional Optimization and Control Theory, Cambridge University Press, Cambridge.10.1017/CBO9780511574795Search in Google Scholar

Fletcher R. and Leyffer, S. (2002). Nonlinear programming without a penalty function, Mathematical Programming, Series A 91(2): 239-269.10.1007/s101070100244Search in Google Scholar

Fletcher, R., Leyffer, and Toint, P. L. (2002a). On the global convergence of a filter-SQP algorithm, SIAM Journal on Optimization 13(1): 44-59.10.1137/S105262340038081XSearch in Google Scholar

Fletcher R., Gould, N. I. M., Leyffer, S., Toint, Ph.L. and Wachter, A. (2002b). Global convergence of trust-region SQP-filter algorithms for general nonlinear programming, SIAM Journal on Optimization 13(3): 635-659.10.1137/S1052623499357258Search in Google Scholar

Fletcher, R. (2010). The sequential quadratic programming method, in G. Di Pillo and F. Schoen (Eds.), Nonlinear Optimization, Lecture Notes in Mathematics, Vol. 1989, Springer-Verlag, Berlin/Heidelberg.10.1007/978-3-642-11339-0_3Search in Google Scholar

Han, J. and Papalambros, P. Y. (2010). An SLP Filter algorithm for probabilistic analytical target cascading, Structural and Multidisciplinary Optimization 41(5): 935-945.10.1007/s00158-009-0450-9Search in Google Scholar

Hinze, M., Pinnau, R., Ulbrich, M. and Ulbrich S. (2009). Optimization with PDE Constraints, Springer, Berlin/Heidelberg.Search in Google Scholar

Lasiecka, I. and Triggiani, R. (2000). Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Vol. I: Abstract Parabolic Systems, Vol. II: Abstract Hyperbolic-Like Systems over a Finite Time Horizon, Encyclopedia of Mathematics and Its Applications, Vol. 74, Cambridge University Press, Cambridge.Search in Google Scholar

Lasiecka, I. and Chueshow, I. (2010). Von Karman Evolution Equations: Well-posedness and Long Time Dynamics, Springer, Berlin/Heidelberg.10.1007/978-0-387-87712-9Search in Google Scholar

Lasiecka, I. and Chueshow I. (2008). Long-time Behavior of Second Order Evolution Equations with Nonlinear Damping, Memoirs of the American Mathematical Society, Philadephia, PA.10.1090/memo/0912Search in Google Scholar

Li, D. (2006). A new SQP-filter method for solving nonlinear programming problems, Journal of Computational Mathematics 24(5): 609-634.Search in Google Scholar

Nie, P. and Ma, C. (2006). A trust-region filter method for general non-linear programming, Applied Mathematics and Computation 172(2): 1000-1017.10.1016/j.amc.2005.03.004Search in Google Scholar

Nettaanmaki P. and Tiba, D. (1994). Optimal Control of Nonlinear Parabolic Systems, Marcel Dekker, New York, NY.Search in Google Scholar

Nocedal J. and Wright, S. J. (2006). Numerical Optimization, Springer, Berlin/Heidelberg.Search in Google Scholar

Perona, P. and Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7): 629-639.10.1109/34.56205Search in Google Scholar

Rafajłowicz, E. (2008). Testing homogeneity of coefficients in distributed systems with application to quality monitoring, IEEE Transactions on Control Systems Technology 16: 314-321.10.1109/TCST.2007.903398Search in Google Scholar

Rafajłowicz, E. and Rafajłowicz, W. (2010). Testing (non-)linearity of distributed-parameter systems from a video sequence, Asian Journal of Control 12(2): 453-461.10.1002/asjc.172Search in Google Scholar

Schittkowski, K. (2002). Numerical Data Fitting in Dynamical Systems; A Practical Introduction with Applications and Software, Applied Optimization, Vol. 77, Kluwer Academic Publishers, Dordrecht.Search in Google Scholar

Schittkowski, K. (2009). An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints, Applied Numerical Mathematics 59(12): 2999-3007.10.1016/j.apnum.2009.07.009Search in Google Scholar

Shen, C., Xue, W. and Pu, D. (2009). Global convergence of a tridimensional filter SQP algorithm based on the line search method, Applied Numerical Mathematics 59(2): 235-250.10.1016/j.apnum.2008.01.005Search in Google Scholar

Shen, C., Xue, W. and Chen, X. (2010). Global convergence of a robust filter SQP algorithm, European Journal of Operational Research 206(1): 34-45.10.1016/j.ejor.2010.02.031Search in Google Scholar

Skowron, M. and Styczeń, K., (2009). Evolutionary search for globally optimal stable multicycles in complex systems with inventory couplings, International Journal of Chemical Engineering, Article ID 137483, DOI:10.1155/2009/137483.10.1155/2009/137483Search in Google Scholar

Su, K. and Che, J. (2007). A modified SQP-filter method and its global convergence, Applied Mathematics and Computation 194(1): 92-101.10.1016/j.amc.2007.04.014Search in Google Scholar

Su, K. and Yu, Z. (2009). A modified SQP method with non-monotone technique and its global convergence, Computers and Mathematics with Applications 57(2): 240-247.10.1016/j.camwa.2008.05.030Search in Google Scholar

Troltzsch, F. (2010). Optimal Control of Partial Differential Equations. Theory, Methods and Applications, American Mathematical Society Press, Providence, RI.10.1090/gsm/112Search in Google Scholar

Turco, A. (2010). Adaptive filter SQP, in C. Blum and R. Battiti (Eds.), Learning and Intelligent Optimization, Lecture Notes in Computer Science, Vol. 6073, Springer-Verlag, Berlin/Heidelberg, pp. 68-81.10.1007/978-3-642-13800-3_6Search in Google Scholar

Uciński, D. (2005). Optimal Measurement Methods for Distributed Parameter System Identification, CRC Press, London/New York, NY.10.1201/9780203026786Search in Google Scholar

Ulbrich, S. (2004). On the superlinear local convergence of a filter-SQP method, Mathematical Programming, Series B 100(1): 217-245.10.1007/s10107-003-0491-6Search in Google Scholar