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A projected gradient and constraint linearization method for nonlinear model predictive control. (English) Zbl 1391.90581
MSC:
90C30 Nonlinear programming
90C55 Methods of successive quadratic programming type
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[1] D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, MA, 1999.
[2] P. T. Boggs and J. W. Tolle, Sequential quadratic programming, Acta Numer., 4 (1995), pp. 1–51. · Zbl 0828.65060
[3] P. T. Boggs, J. W. Tolle, and P. Wang, On the local convergence of quasi-Newton methods for constrained optimization, SIAM J. Control Optim., 20 (1982), pp. 161–171. · Zbl 0494.65036
[4] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, New York, 2004. · Zbl 1058.90049
[5] C. G. Broyden, J. E. Dennis, and J. J. Moré, On the local and superlinear convergence of quasi-Newton methods, IMA J. Appl. Math., 12 (1973), pp. 223–245. · Zbl 0282.65041
[6] H. Chen and F. Allgöwer, A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability, Automatica J. IFAC, 34 (1998), pp. 1205–1217. · Zbl 0947.93013
[7] T. F. Coleman, On characterizations of superlinear convergence for constrained optimization, in Computational Solution of Nonlinear Systems of Equations, E. Allgower, ed., American Mathematical Society, Providence, RI, 1990, pp. 113–133.
[8] R. H. Day, Recursive Programming and Production Response, North-Holland Amsterdam, 1963.
[9] S. de Oliveira Kothare and M. Morari, Contractive model predictive control for constrained nonlinear systems, IEEE Trans. Automat. Control, 45 (2000), pp. 1053–1071. · Zbl 0976.93025
[10] R. S. Dembo, S. C. Eisenstat, and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal., 19 (1982), pp. 400–408. · Zbl 0478.65030
[11] J. E. Dennis, Jr, and J. J. Moré, Quasi-Newton methods, motivation and theory, SIAM Rev., 19 (1977), pp. 46–89.
[12] J. E. Dennis, Jr, and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, 16, SIAM, Classics Appl. Math Philadelphia, 1996.
[13] M. Diehl, H. Bock, J. Schlöder, R. Findeisen, Z. Nagy, and F. Allgöwer, Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations, J. Process Control, 12 (2002), pp. 577–585.
[14] M. Diehl, R. Findeisen, F. Allgöwer, H. G. Bock, and J. P. Schlöder, Nominal stability of real-time iteration scheme for nonlinear model predictive control, IEE Proc. Control Theory, 152 (2005), pp. 296–308.
[15] A. Domahidi and J. Jerez, FORCES Professional, embotech GmbH, , July 2014.
[16] A. Domahidi, A. U. Zgraggen, M. N. Zeilinger, M. Morari, and C. N. Jones, Efficient interior point methods for multistage problems arising in receding horizon control, in Proceedings of the IEEE Conference on Decision and Control, 2012, pp. 668–674.
[17] H. J. Ferreau, H. G. Bock, and M. Diehl, An online active set strategy to overcome the limitations of explicit MPC, Internat. J. Robust Nonlinear Control, 18 (2008), pp. 816–830. · Zbl 1284.93100
[18] A. V. Fiacco, Sensitivity analysis for nonlinear programming using penalty methods, Math. Program., 10 (1976), pp. 287–311. · Zbl 0357.90064
[19] R. Fletcher, A class of methods for nonlinear programming. III. Rates of convergence, in Numerical Methods for Nonlinear Optimitation, F. A. Lootsma, ed., Academic Press, New York, 1972, pp. 371–382.
[20] S. Ghadimi and G. Lan, Accelerated gradient methods for nonconvex nonlinear and stochastic programming, Math. Program., 156 (2016), pp. 59–99. · Zbl 1335.62121
[21] P. E. Gill, W. Murray, and M. A. Saunders, SNOPT: An SQP algorithm for large-scale constrained optimization, SIAM Rev., 47 (2005), pp. 99–131. · Zbl 1210.90176
[22] P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright, Some theoretical properties of an augmented Lagrangian merit function, in Advances in Optimization and Parallel Computing, North-Holland, Amsterdam, 1992, pp. 101–128. · Zbl 0814.90094
[23] J. Goodman, Newton’s method for constrained optimization, Math. Program., 33 (1985), pp. 162–171. · Zbl 0589.90065
[24] S.-P. Han, Superlinearly convergent variable metric algorithms for general nonlinear programming problems, Math. Program., 11 (1976), pp. 263–282. · Zbl 0364.90097
[25] K. Holmström, The TOMLAB optimization environment in Matlab, Adv. Model. Optim., 1 (1999), pp. 47–69.
[26] K. C. Kiwiel, An algorithm for linearly constrained convex nondifferentiable minimization problems, J. Math. Anal. Appl., 105 (1985), pp. 452–465. · Zbl 0564.90053
[27] F. Leibfritz and E. W. Sachs, Inexact SQP interior point methods and large scale optimal control problems, SIAM J. Control Optim., 38 (1999), pp. 272–293. · Zbl 0946.65047
[28] C. Lemaréchal, A view of line-searches, in Optimization and Optimal Control, Springer-Verlag, Berlin 1981, pp. 59–78.
[29] M. Morari and J. H. Lee, Model predictive control: past, Present and future, Comput. Chem. Eng., 23 (1999), pp. 667–682.
[30] W. Murray and F. J. Prieto, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590–640. · Zbl 0840.65052
[31] Y. Nesterov, A method of solving a convex programming problem with convergence rate O (1/k2), Doklady Math., 27 (1983), pp. 372–376. · Zbl 0535.90071
[32] Y. Nesterov, Introductory lectures on convex optimization: A basic course, Appl. Optim. 87, Springer, New York, 2013. · Zbl 1086.90045
[33] J. Nocedal, Updating quasi-Newton matrices with limited storage, Math. Comp., 35 (1980), pp. 773–782. · Zbl 0464.65037
[34] J. Nocedal, Theory of algorithms for unconstrained optimization, Acta Numer., 1 (1992), pp. 199–242. · Zbl 0766.65051
[35] J. Nocedal and S. Wright, Numerical Optimization, Springer-Verlag, Berlin, 1999. · Zbl 0930.65067
[36] F. Palacios-Gomez, L. Lasdon, and M. Engquist, Nonlinear optimization by successive linear programming, Manag. Sci., 28 (1982), pp. 1106–1120. · Zbl 0507.90080
[37] M. J. Powell, A fast algorithm for nonlinearly constrained optimization calculations, in Numerical Analysis, G. A. Watson, ed., Springer-Verlag, Berlin, 1978, pp. 144–157.
[38] M. J. Powell and Y. Yuan, A recursive quadratic programming algorithm that uses differentiable exact penalty functions, Math. Program., 35 (1986), pp. 265–278. · Zbl 0598.90079
[39] R. Quirynen, S. Gros, B. Houska, and M. Diehl, Lifted collocation integrators for direct optimal control in ACADO toolkit, Math. Program. Comput., 9 (2017), pp. 527–571. · Zbl 1387.65057
[40] S. Richter, C. N. Jones, and M. Morari, Real-time input-constrained MPC using fast gradient methods, in Proceedings of the IEEE Conference on Decision and Control and Chinese Control Conference, 2009, pp. 7387–7393.
[41] S. M. Robinson, Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms, Math. Program., 7 (1974), pp. 1–16. · Zbl 0294.90078
[42] J. B. Rosen, The gradient projection method for nonlinear programming. Part II. Nonlinear constraints, SIAM J. Appl. Math., 9 (1961), pp. 514–532. · Zbl 0231.90048
[43] R. Tapia, A stable approach to Newton’s method for general mathematical programming problems in \(\mathbb{R}^n\), J. Optim. Theory Appl., 14 (1974), pp. 453–476. · Zbl 0272.65045
[44] R. Tapia, Quasi-Newton methods for equality constrained optimization: Equivalence of existing methods and a new implementation, in Nonlinear Programming 3 Nonlinear Programming 3, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Elsevier, New York, 1978, pp. 125–164. · Zbl 0469.49026
[45] M. J. Tenny, S. J. Wright, and J. B. Rawlings, Nonlinear model predictive control via feasibility-perturbed sequential quadratic programming, Comput. Optim. Appl., 28 (2004), pp. 87–121. · Zbl 1056.90140
[46] G. Torrisi, Low-Complexity Numerical Methods for Nonlinear Model Predictive Control, Ph.D. thesis, ETH Zurich, 2017, .
[47] G. Torrisi, D. Frick, T. Robbiani, S. Grammatico, R. S. Smith, and M. Morari, FalcOpt: First-order Algorithm via Linearization of Constraints for OPTimization, , May 2017.
[48] G. Torrisi, S. Grammatico, D. Frick, T. Robbiani, R. S. Smith, and M. Morari, Low-complexity first-order constraint linearization methods for efficient nonlinear MPC, in Proceedings of the IEEE Conference on Decision and Control, 2017, pp. 4376–4381.
[49] G. Torrisi, S. Grammatico, R. S. Smith, and M. Morari, A variant to sequential quadratic programming for nonlinear model predictive control, in Proceedings of the IEEE Conference on Decision and Control, 2016, pp. 2814–2819.
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