## TRICE

 swMATH ID: 5197 Software Authors: Dennis, J.E.; Heinkenschloss, Matthias; Vicente, Lu'{i}s N. Description: Trust-region interior-point SQP algorithms for a class of nonlinear programming problems A family of trust-region interior-point sequential quadratic programming (SQP) algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise, e.g., from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations.par The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed, for a different class of problems, by {it T. F. Coleman} and {it Y. Li} [SIAM J. Optim. 6, 418-445 (1996; Zbl 0855.65063)] and they exploit trust-region techniques for equality-constrained optimization. Thus, they allow the computation of the steps using a variety of methods, including many iterative techniques.par Global convergence of these algorithms to a first-order Karush-Kuhn-Tucker (KKT) limit point is proved under very mild conditions on the trial steps. Under reasonable, but more stringent, conditions on the quadratic model and on the trial steps, the sequence of iterates generated by the algorithms is shown to have a limit point satisfying the second-order necessary KKT conditions. The local rate of convergence to a nondegenerate strict local minimizer is $$q$$-quadratic. The results given here include, as special cases, current results for only equality constraints and for only simple bounds.par Numerical results for the solution of an optimal control problem governed by a nonlinear heat equation are reported. Homepage: http://www.caam.rice.edu/~trice/ Keywords: nonlinear programming; SQP methods; trust-region methods; interior-point algorithms; Dikin-Karmarkar ellipsoid; Coleman-Li affine scaling; simple bounds; optimal control problems Related Software: LANCELOT; Ipopt; SNOPT; CUTEr; TRON; NPSOL; LOQO; LSQR; ipfilter; SifDec; NewtonLib; L-BFGS; CUTE; QSDPNAL; HSolver; PENLAB; z3; LMIRank; Benchmarks; RSOLVER Cited in: 46 Publications
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### Cited by 85 Authors

 5 Vicente, Luis Nunes 3 Heinkenschloss, Matthias 2 Avelino, Catarina Pina 2 Dennis, John E. jun. 2 Lucidi, Stefano 2 Yabe, Hiroshi 2 Yamashita, Hiroshi 1 Andreani, Roberto 1 Antil, Harbir 1 Ascher, Uri M. 1 Audet, Charles 1 Birgin, Ernesto G. 1 Bonnans, Joseph Frédéric 1 Burger, Martin 1 Chen, Lifeng 1 Chen, Mingshuai 1 Cliff, Eugene M. 1 Coleman, Thomas F. 1 Cristofari, Andrea 1 De Santis, Marianna 1 DiPillo, Gianni 1 El-Alem, Mahmoud M. 1 El-Sayed, Salah M. 1 El-Sobky, Bothina 1 Gertz, E. Michael 1 Gilbert, Jean Charles 1 Gill, Philip E. 1 Goldfarb, Donald 1 Gonzaga, Clovis C. 1 Gould, Nicholas Ian Mark 1 Haber, Eldad 1 Hager, William W. 1 Henrion, René 1 Herrmann, Felix J. 1 Hintermüller, Michael 1 Hinze, Michael 1 Hoppe, Ronald H. W. 1 Hosseini, Mohammad-Mehdi 1 Hribar, Mary E. 1 Karas, Elizabeth W. 1 Katoen, Joost-Pieter 1 Kunisch, Karl 1 Lantoine, Gregory 1 Lee, Hyung-Chun 1 Leibfritz, Friedemann 1 Li, Yuying 1 Liepelt, Michael 1 Linsenmann, Christopher 1 Liu, Xinwei 1 Lu, Wenting 1 Ma, Yanbo 1 Maalek Ghaini, Farid Mohammad 1 Martínez, José Mario 1 Möller, Andris 1 Mostafa, El-Sayed M. E. 1 Mühlhuber, Wolfram 1 Nocedal, Jorge 1 Oldenburg, Doug 1 Orban, Dominique 1 Palagi, Laura 1 Plantenga, Todd 1 Pola, Cecilia 1 Rahmanpour, Fardin 1 Rinaldi, Francesco 1 Russell, Ryan P. 1 Sartenaer, Annick 1 Schittkowski, Klaus 1 Schuverdt, María Laura 1 Shenoy, Ajit R. 1 Tanabe, Takahito 1 Tong, Xiaojiao 1 Tseng, Paul 1 Ulbrich, Michael 1 Ulbrich, Stefan 1 van Leeuwen, Tristan 1 Volkwein, Stefan 1 Wang, Qiuye 1 Xue, Bai 1 Yao, Yirong 1 Yuan, Ya-xiang 1 Zhan, Naijun 1 Zhang, Hongchao 1 Zhang, Liansheng 1 Zhou, Shuzi 1 Zhu, Zhibin
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### Cited in 24 Serials

 6 Mathematical Programming. Series A. Series B 6 SIAM Journal on Optimization 5 Journal of Optimization Theory and Applications 3 SIAM Journal on Control and Optimization 2 Inverse Problems 2 Applied Mathematics and Computation 2 SIAM Journal on Scientific Computing 1 Computers & Mathematics with Applications 1 Mathematics of Operations Research 1 SIAM Journal on Numerical Analysis 1 Optimal Control Applications & Methods 1 Japan Journal of Industrial and Applied Mathematics 1 European Journal of Operational Research 1 Linear Algebra and its Applications 1 Computational Optimization and Applications 1 Applied Mathematics. Series B (English Edition) 1 Turkish Journal of Mathematics 1 International Journal of Computational Fluid Dynamics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Optimization Methods & Software 1 Journal of Shanghai University 1 Journal of Numerical Mathematics 1 Journal of Applied Mathematics and Computing 1 Journal of Nonlinear Science and Applications
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### Cited in 11 Fields

 41 Operations research, mathematical programming (90-XX) 20 Numerical analysis (65-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 5 Partial differential equations (35-XX) 5 Fluid mechanics (76-XX) 5 Systems theory; control (93-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX)