# zbMATH — the first resource for mathematics

## Ralph, Daniel

Compute Distance To:
 Author ID: ralph.daniel Published as: Ralph, D.; Ralph, Daniel
 Documents Indexed: 54 Publications since 1993, including 4 Books
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#### Co-Authors

 6 single-authored 6 Pang, Jong-Shi 5 Jiang, Houyuan 5 Luo, Zhi-Quan 4 Ferris, Michael C. 4 Wright, Stephen J. 3 Eberhard, Andrew C. 2 Churilov, Leonid 2 Crouzeix, Jean-Pierre 2 Hu, Xinmin 2 Scholtes, Stefan 2 Sniedovich, Moshe 1 Boland, Natashia L. 1 Bomze, Immanuel M. 1 Facchinei, Francisco 1 Giallombardo, Giovanni 1 Glover, Barney M. 1 Goulart, Paul J. 1 Hill, Robin D. 1 Holmberg, Pär 1 Hult, Edward 1 Kerrigan, Eric C. 1 Munson, Todd S. 1 Neame, Philip J. 1 Newbery, David M. G. 1 Parpas, Panos 1 Sim, Chee-Khian 1 Smeers, Yves 1 Stein, Oliver 1 Sun, Jie 1 Wiesemann, Wolfram 1 Wu, Shiquan 1 Xu, Huifu
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#### Serials

 11 Mathematical Programming. Series A. Series B 6 Mathematics of Operations Research 3 SIAM Journal on Optimization 3 Computational Optimization and Applications 1 Journal of Economic Theory 1 Journal of Optimization Theory and Applications 1 Operations Research 1 Operations Research Letters 1 Asia-Pacific Journal of Operational Research 1 Linear Algebra and its Applications 1 Optimization Methods & Software 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Applied Optimization 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 39 Operations research, mathematical programming (90-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General and overarching topics; collections (00-XX) 4 Numerical analysis (65-XX) 2 Real functions (26-XX) 2 Systems theory; control (93-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH

46 Publications have been cited 895 times in 701 Documents Cited by Year
Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints. Zbl 0870.90092
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel; Wu, Shi-Quan
1996
Mathematical programs with equilibrium constraints. Reprint of the 1997 hardback ed. Zbl 1139.90003
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel
2008
Mathematical programs with equilibrium constraints. Zbl 0898.90006
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel
1997
Smooth SQP methods for mathematical programs with nonlinear complementarity constraints. Zbl 0955.90134
Jiang, Houyuan; Ralph, Daniel
2000
Piecewise smoothness, local invertibility, and parametric analysis of normal maps. Zbl 0857.90122
Pang, Jong-Shi; Ralph, Daniel
1996
Using EPECs to model bilevel games in restructured electricity markets with locational prices. Zbl 1167.91357
Hu, Xinmin; Ralph, Daniel
2007
Some properties of regularization and penalization schemes for MPECs. Zbl 1097.90054
Ralph, Daniel; Wright, Stephen J.
2004
Directional derivatives of the solution of a parametric nonlinear program. Zbl 0844.90089
Ralph, D.; Dempe, S.
1995
Global convergence of damped Newton’s method for nonsmooth equations via the path search. Zbl 0819.90102
Ralph, Daniel
1994
OPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints. Zbl 1040.90500
Jiang, Houyuan; Ralph, Daniel
1999
A superlinear infeasible-interior-point algorithm for monotone complementarity problems. Zbl 0867.90112
Wright, Stephen; Ralph, Daniel
1996
Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition. Zbl 1273.90113
Wogrin, S.; Hobbs, B. F.; Ralph, D.; Centeno, E.; Barquín, J.
2013
Extension of quasi-Newton methods to mathematical programs with complementarity constraints. Zbl 1038.90100
Jiang, Houyuan; Ralph, Daniel
2003
Small convex-valued subdifferentials in mathematical programming. Zbl 0816.49007
Craven, B. D.; Ralph, D.; Glover, B. M.
1995
Convergence of stationary points of sample average two-stage stochastic programs: a generalized equation approach. Zbl 1246.90110
Ralph, Daniel; Xu, Huifu
2011
Sensitivity analysis of composite piecewise smooth equations. Zbl 0871.90094
Ralph, Daniel; Scholtes, Stefan
1997
Implicit smoothing and its application to optimization with piecewise smooth equality constraints. Zbl 1211.90278
Ralph, D.; Xu, H.
2005
A geometrical insight on pseudoconvexity and pseudomonotonicity. Zbl 1189.26019
Crouzeix, Jean-Pierre; Eberhard, Andrew; Ralph, Daniel
2010
Superlinear convergence of an interior-point method for monotone variational inequalities. Zbl 0886.90162
Ralph, Daniel; Wright, Stephen J.
1997
Projected gradient methods for nonlinear complementarity problems via normal maps. Zbl 0946.90090
Ferris, Michael C.; Ralph, Daniel
1995
A note on sensitivity of value functions of mathematical programs with complementarity constraints. Zbl 1065.90072
Hu, Xinmin; Ralph, Daniel
2002
Superlinear convergence of an interior-point method despite dependent constraints. Zbl 0977.90082
Ralph, Daniel; Wright, Stephen J.
2000
Global and local superlinear convergence analysis of Newton-type methods for semismooth equations with smooth least squares. Zbl 0928.65060
Jiang, Houyuan; Ralph, Daniel
1999
Sequential quadratic programming for mathematical programs with linear complementarity constraints. Zbl 0910.90253
Ralph, D.
1996
On branching numbers of normal manifolds. Zbl 0830.57014
Ralph, Daniel
1994
Supply function equilibria: step functions and continuous representations. Zbl 1285.91103
Holmberg, Pär; Newbery, David; Ralph, Daniel
2013
A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister function. Zbl 1111.90112
Sim, Chee-Khian; Sun, Jie; Ralph, Daniel
2006
An outer approximate subdifferential method for piecewise affine optimization. Zbl 0959.90047
Neame, Philip; Boland, Natashia; Ralph, Daniel
2000
Piecewise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints. Zbl 0897.90184
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel
1998
A new proof of Robinson’s homeomorphism theorem for pl-normal maps. Zbl 0770.90069
Ralph, Daniel
1993
Mathematical programs with complementarity constraints in traffic and telecommunications networks. Zbl 1153.90361
Ralph, Daniel
2008
A stable homotopy approach to horizontal linear complementary problems. Zbl 1117.90069
Ralph, D.
2002
A nonlinear duality result equivalent to the Clarke-Ledyaev mean value inequality. Zbl 0844.49014
Lewis, A. S.; Ralph, D.
1996
First order approximations to nonsmooth mappings with application to metric regularity. Zbl 0811.49014
Glover, B. M.; Ralph, D.
1994
Risk trading and endogenous probabilities in investment equilibria. Zbl 1372.91130
Ralph, Daniel; Smeers, Yves
2015
Efficient robust optimization for robust control with constraints. Zbl 1143.49025
Goulart, Paul J.; Kerrigan, Eric C.; Ralph, Daniel
2008
Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs. Zbl 1145.90073
Giallombardo, Giovanni; Ralph, Daniel
2008
A chain rule for nonsmooth composite functions via minimisation. Zbl 0829.49015
Ralph, D.
1994
The C-index: a new stability concept for quadratic programs with complementarity constraints. Zbl 1243.90219
Ralph, Daniel; Stein, Oliver
2011
Characterizations for perturbed exact penalty functions. Zbl 1090.90183
Yang, X. Q.; Ralph, D.
2005
A note on composite concave quadratic programming. Zbl 0941.90059
Churilov, Leonid; Ralph, Daniel; Sniedovich, Moshe
1998
(Convex) level sets integration. Zbl 1390.26022
Crouzeix, Jean-Pierre; Eberhard, Andrew; Ralph, Daniel
2016
Exact computational approaches to a stochastic uncapacitated single allocation $$p$$-hub center problem. Zbl 1302.90237
Hult, Edward; Jiang, Houyuan; Ralph, Daniel
2014
Hyper sensitivity analysis of portfolio optimization problems. Zbl 1059.91037
Churilov, Leonid; Bomze, Immanuel M.; Sniedovich, Moshe; Ralph, Daniel
2004
Dual-sampling-rate moving-horizon control of a class of linear systems with input saturation and plant uncertainty. Zbl 1040.93054
Brockwell, A.; Polak, E.; Evans, R.; Ralph, D.
2003
A homotopy method for mixed complementarity problems based on the PATH solver. Zbl 0952.65050
Ferris, M. C.; Munson, T. S.; Ralph, D.
2000
(Convex) level sets integration. Zbl 1390.26022
Crouzeix, Jean-Pierre; Eberhard, Andrew; Ralph, Daniel
2016
Risk trading and endogenous probabilities in investment equilibria. Zbl 1372.91130
Ralph, Daniel; Smeers, Yves
2015
Exact computational approaches to a stochastic uncapacitated single allocation $$p$$-hub center problem. Zbl 1302.90237
Hult, Edward; Jiang, Houyuan; Ralph, Daniel
2014
Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition. Zbl 1273.90113
Wogrin, S.; Hobbs, B. F.; Ralph, D.; Centeno, E.; Barquín, J.
2013
Supply function equilibria: step functions and continuous representations. Zbl 1285.91103
Holmberg, Pär; Newbery, David; Ralph, Daniel
2013
Convergence of stationary points of sample average two-stage stochastic programs: a generalized equation approach. Zbl 1246.90110
Ralph, Daniel; Xu, Huifu
2011
The C-index: a new stability concept for quadratic programs with complementarity constraints. Zbl 1243.90219
Ralph, Daniel; Stein, Oliver
2011
A geometrical insight on pseudoconvexity and pseudomonotonicity. Zbl 1189.26019
Crouzeix, Jean-Pierre; Eberhard, Andrew; Ralph, Daniel
2010
Mathematical programs with equilibrium constraints. Reprint of the 1997 hardback ed. Zbl 1139.90003
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel
2008
Mathematical programs with complementarity constraints in traffic and telecommunications networks. Zbl 1153.90361
Ralph, Daniel
2008
Efficient robust optimization for robust control with constraints. Zbl 1143.49025
Goulart, Paul J.; Kerrigan, Eric C.; Ralph, Daniel
2008
Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs. Zbl 1145.90073
Giallombardo, Giovanni; Ralph, Daniel
2008
Using EPECs to model bilevel games in restructured electricity markets with locational prices. Zbl 1167.91357
Hu, Xinmin; Ralph, Daniel
2007
A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister function. Zbl 1111.90112
Sim, Chee-Khian; Sun, Jie; Ralph, Daniel
2006
Implicit smoothing and its application to optimization with piecewise smooth equality constraints. Zbl 1211.90278
Ralph, D.; Xu, H.
2005
Characterizations for perturbed exact penalty functions. Zbl 1090.90183
Yang, X. Q.; Ralph, D.
2005
Some properties of regularization and penalization schemes for MPECs. Zbl 1097.90054
Ralph, Daniel; Wright, Stephen J.
2004
Hyper sensitivity analysis of portfolio optimization problems. Zbl 1059.91037
Churilov, Leonid; Bomze, Immanuel M.; Sniedovich, Moshe; Ralph, Daniel
2004
Extension of quasi-Newton methods to mathematical programs with complementarity constraints. Zbl 1038.90100
Jiang, Houyuan; Ralph, Daniel
2003
Dual-sampling-rate moving-horizon control of a class of linear systems with input saturation and plant uncertainty. Zbl 1040.93054
Brockwell, A.; Polak, E.; Evans, R.; Ralph, D.
2003
A note on sensitivity of value functions of mathematical programs with complementarity constraints. Zbl 1065.90072
Hu, Xinmin; Ralph, Daniel
2002
A stable homotopy approach to horizontal linear complementary problems. Zbl 1117.90069
Ralph, D.
2002
Smooth SQP methods for mathematical programs with nonlinear complementarity constraints. Zbl 0955.90134
Jiang, Houyuan; Ralph, Daniel
2000
Superlinear convergence of an interior-point method despite dependent constraints. Zbl 0977.90082
Ralph, Daniel; Wright, Stephen J.
2000
An outer approximate subdifferential method for piecewise affine optimization. Zbl 0959.90047
Neame, Philip; Boland, Natashia; Ralph, Daniel
2000
A homotopy method for mixed complementarity problems based on the PATH solver. Zbl 0952.65050
Ferris, M. C.; Munson, T. S.; Ralph, D.
2000
OPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints. Zbl 1040.90500
Jiang, Houyuan; Ralph, Daniel
1999
Global and local superlinear convergence analysis of Newton-type methods for semismooth equations with smooth least squares. Zbl 0928.65060
Jiang, Houyuan; Ralph, Daniel
1999
Piecewise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints. Zbl 0897.90184
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel
1998
A note on composite concave quadratic programming. Zbl 0941.90059
Churilov, Leonid; Ralph, Daniel; Sniedovich, Moshe
1998
Mathematical programs with equilibrium constraints. Zbl 0898.90006
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel
1997
Sensitivity analysis of composite piecewise smooth equations. Zbl 0871.90094
Ralph, Daniel; Scholtes, Stefan
1997
Superlinear convergence of an interior-point method for monotone variational inequalities. Zbl 0886.90162
Ralph, Daniel; Wright, Stephen J.
1997
Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints. Zbl 0870.90092
Luo, Zhi-Quan; Pang, Jong-Shi; Ralph, Daniel; Wu, Shi-Quan
1996
Piecewise smoothness, local invertibility, and parametric analysis of normal maps. Zbl 0857.90122
Pang, Jong-Shi; Ralph, Daniel
1996
A superlinear infeasible-interior-point algorithm for monotone complementarity problems. Zbl 0867.90112
Wright, Stephen; Ralph, Daniel
1996
Sequential quadratic programming for mathematical programs with linear complementarity constraints. Zbl 0910.90253
Ralph, D.
1996
A nonlinear duality result equivalent to the Clarke-Ledyaev mean value inequality. Zbl 0844.49014
Lewis, A. S.; Ralph, D.
1996
Directional derivatives of the solution of a parametric nonlinear program. Zbl 0844.90089
Ralph, D.; Dempe, S.
1995
Small convex-valued subdifferentials in mathematical programming. Zbl 0816.49007
Craven, B. D.; Ralph, D.; Glover, B. M.
1995
Projected gradient methods for nonlinear complementarity problems via normal maps. Zbl 0946.90090
Ferris, Michael C.; Ralph, Daniel
1995
Global convergence of damped Newton’s method for nonsmooth equations via the path search. Zbl 0819.90102
Ralph, Daniel
1994
On branching numbers of normal manifolds. Zbl 0830.57014
Ralph, Daniel
1994
First order approximations to nonsmooth mappings with application to metric regularity. Zbl 0811.49014
Glover, B. M.; Ralph, D.
1994
A chain rule for nonsmooth composite functions via minimisation. Zbl 0829.49015
Ralph, D.
1994
A new proof of Robinson’s homeomorphism theorem for pl-normal maps. Zbl 0770.90069
Ralph, Daniel
1993
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#### Cited by 959 Authors

 25 Pang, Jong-Shi 21 Zhang, Liwei 19 Lin, Guihua 16 Kanzow, Christian 16 Xu, Huifu 15 Fukushima, Masao 12 Outrata, Jiří V. 12 Ralph, Daniel 12 Ye, Jane J. 11 Qi, Liqun 11 Yang, Xiaoqi 9 Chen, Xiaojun 9 Dempe, Stephan 9 Schmidt, Martin 9 Zhang, Jin 8 Chiou, Suh-Wen 8 Lin, Lai-Jiu 8 Mordukhovich, Boris S. 8 Schwartz, Alexandra 8 Sun, Defeng 8 Wu, Jia 7 Barton, Paul I. 7 Červinka, Michal 7 Ferris, Michael C. 7 Júdice, Joaquim João 7 Lin, Gui-Hua 7 Liu, Guoshan 7 Sun, Hailin 7 Tin-Loi, Francis 7 Yao, Yonghong 7 Zhang, Jie 7 Zhang, Yi 7 Zhu, Xide 6 Andreani, Roberto 6 Chen, Jein-Shan 6 Gao, Yan 6 Hintermüller, Michael 6 Hobbs, Benjamin F. 6 Hoheisel, Tim 6 Huang, Xuexiang 6 Liu, Yongchao 6 Noor, Muhammad Aslam 6 Schewe, Lars 6 Zhang, Dali 6 Zhang, Jianzhong 5 Aussel, Didier 5 Facchinei, Francisco 5 Guo, Lei 5 Han, Jiye 5 Henrion, René 5 Le Thi, Hoai An 5 Liou, Yeongcheng 5 Martínez, José Mario 5 Pang, Liping 5 Pham Dinh Tao 5 Stechlinski, Peter G. 5 Still, Georg J. 5 Sun, Jie 4 Ali, Rehan 4 Ansari, Qamrul Hasan 4 Bouza-Allende, Gemayqzel 4 Ceng, Lu-Chuan 4 Gadhi, Nazih Abderrazzak 4 Glover, Bevil Milton 4 Grimm, Veronika 4 Izmailov, Alexey F. 4 Jian, Jinbao 4 Kazmi, Kaleem Raza 4 Leyffer, Sven 4 Lu, Shu 4 Mishra, Shashi Kant 4 Mitchell, John E. 4 Nie, Pu-yan 4 Pan, Shaohua 4 Pištěk, Miroslav 4 Shanbhag, Uday V. 4 Stein, Oliver 4 Surowiec, Thomas 4 Teo, Kok Lay 4 Tseng, Paul 4 Wan, Zhong 4 Wan, Zhongping 4 Yang, Xinmin 4 Zhao, Gongyun 4 Zhu, Zhibin 4 Zöttl, Gregor 3 Bai, Lijie 3 Chen, Jiawei 3 Cho, Yeol Je 3 De los Reyes, Juan Carlos 3 Dutta, Joydeep 3 Gabriel, Steven A. 3 Galligani, Emanuele 3 Hadjisavvas, Nicolas 3 Holmberg, Pär 3 Huang, Zheng-Hai 3 Huppmann, Daniel 3 Iiduka, Hideaki 3 Khan, Kamil A. 3 Li, Guoyin ...and 859 more Authors
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#### Cited in 119 Serials

 91 Journal of Optimization Theory and Applications 66 Mathematical Programming. Series A. Series B 36 Journal of Global Optimization 35 European Journal of Operational Research 35 Computational Optimization and Applications 31 Optimization 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Set-Valued and Variational Analysis 17 Journal of Mathematical Analysis and Applications 14 Applied Mathematics and Computation 14 Optimization Methods & Software 13 Journal of Computational and Applied Mathematics 13 Networks and Spatial Economics 11 Computer Methods in Applied Mechanics and Engineering 11 SIAM Journal on Optimization 10 Numerical Functional Analysis and Optimization 10 Annals of Operations Research 9 Computers & Operations Research 9 Mathematical Methods of Operations Research 9 Journal of Inequalities and Applications 8 Operations Research Letters 8 Numerical Algorithms 7 Kybernetika 7 Journal of Applied Mathematics and Computing 7 Journal of Industrial and Management Optimization 7 Optimization Letters 6 Mathematics of Computation 5 Computers & Mathematics with Applications 5 Asia-Pacific Journal of Operational Research 5 Applications of Mathematics 5 Linear Algebra and its Applications 4 Automatica 4 Applied Mathematics and Mechanics. (English Edition) 4 Mathematical and Computer Modelling 4 Applied Mathematical Modelling 4 Vietnam Journal of Mathematics 4 Optimization and Engineering 4 Fixed Point Theory and Applications 4 Numerical Algebra, Control and Optimization 3 Journal of Economic Theory 3 Mathematics of Operations Research 3 Systems & Control Letters 3 Acta Mathematicae Applicatae Sinica. English Series 3 International Journal of Computer Mathematics 3 Journal of Mathematical Imaging and Vision 3 Set-Valued Analysis 3 Top 3 Mathematical Problems in Engineering 3 RAIRO. Operations Research 3 Computational Management Science 3 Science China. Mathematics 3 Journal of the Operations Research Society of China 3 Nonlinear Analysis. Theory, Methods & Applications 2 Acta Mathematica Vietnamica 2 Calcolo 2 International Journal for Numerical Methods in Engineering 2 Journal of Mathematical Economics 2 Journal of Economic Dynamics & Control 2 Economic Theory 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Discrete Dynamics in Nature and Society 2 Journal of Applied Mathematics 2 Journal of Fixed Point Theory and Applications 2 Mathematical Programming Computation 2 EURO Journal on Computational Optimization 1 Bulletin of the Australian Mathematical Society 1 International Journal of Solids and Structures 1 Journal of the Franklin Institute 1 Applied Mathematics and Optimization 1 Computing 1 Fuzzy Sets and Systems 1 International Journal of Game Theory 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Numerische Mathematik 1 Operations Research 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Journal of Information & Optimization Sciences 1 Mathematical Social Sciences 1 Bulletin of the Iranian Mathematical Society 1 Applied Numerical Mathematics 1 Science in China. Series A 1 Neural Networks 1 Economics Letters 1 Computational Mathematics and Mathematical Physics 1 SIAM Journal on Applied Mathematics 1 Archive of Applied Mechanics 1 International Journal of Robust and Nonlinear Control 1 SIAM Journal on Scientific Computing 1 Computational and Applied Mathematics 1 Journal of Convex Analysis 1 INFORMS Journal on Computing 1 Abstract and Applied Analysis 1 Positivity 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 European Journal of Mechanics. A. Solids 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics ...and 19 more Serials
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#### Cited in 29 Fields

 581 Operations research, mathematical programming (90-XX) 189 Calculus of variations and optimal control; optimization (49-XX) 148 Numerical analysis (65-XX) 122 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Operator theory (47-XX) 21 Mechanics of deformable solids (74-XX) 19 Real functions (26-XX) 12 Systems theory; control (93-XX) 11 Computer science (68-XX) 8 Ordinary differential equations (34-XX) 6 Partial differential equations (35-XX) 6 Convex and discrete geometry (52-XX) 5 Functional analysis (46-XX) 5 Statistics (62-XX) 5 Information and communication theory, circuits (94-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Biology and other natural sciences (92-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 General topology (54-XX) 2 Manifolds and cell complexes (57-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of particles and systems (70-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Geophysics (86-XX)