## Ipopt

 swMATH ID: 4808 Software Authors: Andreas Waechter, Carl Laird Description: Ipopt (Interior Point OPTimizer, pronounced eye-pea-Opt) is a software package for large-scale ​nonlinear optimization. It is designed to find (local) solutions of mathematical optimization problems of the from min f(x), x in R^n s.t. g_L <= g(x) <= g_U, x_L <= x <= x_U, where f(x): R^n –> R is the objective function, and g(x): R^n –> R^m are the constraint functions. The vectors g_L and g_U denote the lower and upper bounds on the constraints, and the vectors x_L and x_U are the bounds on the variables x. The functions f(x) and g(x) can be nonlinear and nonconvex, but should be twice continuously differentiable. Note that equality constraints can be formulated in the above formulation by setting the corresponding components of g_L and g_U to the same value.Ipopt is part of the ​COIN-OR Initiative. Homepage: https://projects.coin-or.org/Ipopt Programming Languages: C++ Operating Systems: Windows, Linux, MacOS Keywords: interior point; continuous optimization; nonlinear programming Related Software: AMPL; SNOPT; SCIP; Bonmin; CPLEX; KNITRO; SOCS; BARON; Gurobi; CUTEr; Matlab; MINLPLib; ANTIGONE; CasADi; LINDO; LANCELOT; ipfilter; GAMS; LOQO; Mosek Referenced in: 793 Publications
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### Referenced by 1,433 Authors

 20 Maurer, Helmut 19 Biegler, Lorenz T. 18 Trélat, Emmanuel 14 Martínez, José Mario 12 Birgin, Ernesto G. 12 Bonami, Pierre 12 Wächter, Andreas 12 Zuazua, Enrique 11 Liberti, Leo 10 Curtis, Frank E. 10 Gleixner, Ambros M. 10 Orban, Dominique 10 Sager, Sebastian 9 Diehl, Moritz Mathias 9 Kaya, C. Yalçin 9 Rao, Anil V. 9 Schenk, Olaf 9 Stoyan, Yuriĭ Grygorovych 8 Armand, Paul 8 Berthold, Timo 8 Kirches, Christian 8 Schmidt, Martin 7 Alvarez-Vázquez, Lino Jose 7 Hijazi, Hassan 7 Leyffer, Sven 7 Privat, Yannick 7 Sahinidis, Nikolaos V. 7 Vigerske, Stefan 6 Benoist, Joël 6 D’Ambrosio, Claudia 6 Fernández, Francisco Javier 6 Hager, William W. 6 Mitsos, Alexander 6 Nocedal, Jorge 6 Torres, Delfim Fernando Marado 6 Weichert, Dieter 5 Belotti, Pietro 5 de Pinho, Maria do Rosário 5 Grossmann, Ignacio E. 5 Júdice, Joaquim João 5 Kronqvist, Jan 5 Lee, Jon 5 Linderoth, Jeff T. 5 Lodi, Andrea 5 Micheletti, Stefano 5 Monteiro, M. Teresa T. 5 Müller, Benjamin 5 Najman, Jaromił 5 Neumaier, Arnold 5 Omheni, Riadh 5 Perotto, Simona 5 Qiu, Songqiang 5 Quirynen, Rien 5 Ulbrich, Michael 5 Walther, Andrea 5 Zhu, Detong 4 Abarbanel, Henry D. I. 4 Andreani, Roberto 4 Anitescu, Mihai 4 Benson, Hande Y. 4 Bock, Hans Georg 4 Bongartz, Dominik 4 Cafieri, Sonia 4 Campbell, Stephen LaVern 4 Chen, Zhongwen 4 Christofides, Panagiotis D. 4 Fernandes, Edite M. G. P. 4 Fernández, Felipe 4 Humpola, Jesco 4 Lebiedz, Dirk 4 Litvinchev, Igor S. 4 Liu, Xinggao 4 Liu, Xinwei 4 Manns, Paul 4 Martinez, Aurea 4 Nannicini, Giacomo 4 Nowak, Ivo 4 Ouorou, Adam 4 Pecci, Filippo 4 Petra, Cosmin G. 4 Robinson, Daniel P. 4 Romanova, Tatiana E. 4 Rumpf, Martin 4 Schuverdt, María Laura 4 Serrano, Felipe 4 Sessa, Valentina 4 Shen, Chungen 4 Silva, Cristiana J. 4 Steinbach, Marc Christian 4 Stoianov, Ivan 4 Tortorelli, Daniel A. 4 Van Hentenryck, Pascal 4 Waltz, Richard A. 3 Alt, Walter 3 Audet, Charles 3 Betts, John T. 3 Blomvall, Jörgen 3 Brust, Johannes J. 3 Burachik, Regina Sandra 3 Carrizosa, Emilio ...and 1,333 more Authors
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### Referenced in 176 Serials

 54 Computational Optimization and Applications 43 Journal of Global Optimization 36 SIAM Journal on Optimization 33 Mathematical Programming. Series A. Series B 31 Journal of Optimization Theory and Applications 30 Optimization and Engineering 27 European Journal of Operational Research 26 Computer Methods in Applied Mechanics and Engineering 24 Mathematical Programming Computation 21 Automatica 16 Optimization Methods & Software 15 SIAM Journal on Scientific Computing 14 INFORMS Journal on Computing 11 Computers & Operations Research 10 Optimal Control Applications & Methods 10 Journal of Industrial and Management Optimization 8 SIAM Journal on Control and Optimization 8 Numerical Algorithms 8 EURO Journal on Computational Optimization 7 Applied Mathematics and Computation 7 Applied Mathematical Modelling 7 Mathematical Biosciences and Engineering 6 International Journal of Control 6 Journal of Computational and Applied Mathematics 6 Operations Research Letters 6 Optimization Letters 5 Operations Research 5 Computer Aided Geometric Design 5 Optimization 5 Annals of Operations Research 5 Cybernetics and Systems Analysis 5 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Computational Physics 4 Journal of Fluid Mechanics 4 Mathematical Biosciences 4 Systems & Control Letters 4 International Journal of Computer Mathematics 4 Top 4 Mathematical Problems in Engineering 4 Multibody System Dynamics 4 Nonlinear Dynamics 4 Vietnam Journal of Mathematics 4 Mathematical Methods of Operations Research 4 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Applied Mathematics and Computing 4 Numerical Algebra, Control and Optimization 3 Computers & Mathematics with Applications 3 Journal of the Franklin Institute 3 ACM Transactions on Mathematical Software 3 International Journal for Numerical Methods in Engineering 3 Acta Applicandae Mathematicae 3 Applied Numerical Mathematics 3 Computational Mechanics 3 Journal of Scientific Computing 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 Discrete and Continuous Dynamical Systems 3 European Journal of Control 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 International Journal of Applied Mathematics and Computer Science 3 Quantitative Finance 3 Discrete and Continuous Dynamical Systems. Series S 3 Mathematical Control and Related Fields 2 Biological Cybernetics 2 Computers and Fluids 2 Communications on Pure and Applied Mathematics 2 Psychometrika 2 Mathematics of Computation 2 Bulletin of Mathematical Biology 2 Applied Mathematics and Optimization 2 Mathematics and Computers in Simulation 2 SIAM Journal on Numerical Analysis 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 ACM Transactions on Graphics 2 Discrete & Computational Geometry 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Journal on Applied Mathematics 2 SIAM Review 2 ETNA. Electronic Transactions on Numerical Analysis 2 CEJOR. Central European Journal of Operations Research 2 Journal of Systems Science and Complexity 2 OR Spectrum 2 Structural and Multidisciplinary Optimization 2 GAMM-Mitteilungen 2 SIAM Journal on Imaging Sciences 2 SIAM/ASA Journal on Uncertainty Quantification 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Archive for Rational Mechanics and Analysis 1 Computer Physics Communications 1 Discrete Applied Mathematics 1 Inverse Problems 1 Journal of Engineering Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Journal of the Mechanics and Physics of Solids 1 Moscow University Mathematics Bulletin 1 Nonlinearity 1 Physics Letters. A 1 Biometrics 1 Control and Cybernetics ...and 76 more Serials
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### Referenced in 39 Fields

 469 Operations research, mathematical programming (90-XX) 241 Calculus of variations and optimal control; optimization (49-XX) 232 Numerical analysis (65-XX) 105 Systems theory; control (93-XX) 63 Biology and other natural sciences (92-XX) 51 Mechanics of deformable solids (74-XX) 43 Computer science (68-XX) 42 Partial differential equations (35-XX) 40 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 28 Statistics (62-XX) 27 Fluid mechanics (76-XX) 21 Ordinary differential equations (34-XX) 19 Mechanics of particles and systems (70-XX) 13 Dynamical systems and ergodic theory (37-XX) 10 Probability theory and stochastic processes (60-XX) 8 Convex and discrete geometry (52-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Information and communication theory, circuits (94-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Real functions (26-XX) 4 Approximations and expansions (41-XX) 4 Geophysics (86-XX) 3 Combinatorics (05-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Functions of a complex variable (30-XX) 2 Functional analysis (46-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 (04-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX)