Edit Profile (opens in new tab) Tapia, Richard A. Co-Author Distance Author ID: tapia.richard-a Published as: Tapia, R. A.; Tapia, Richard A.; Tapia, Richard; Tapia, R. more...less Homepage: https://www.caam.rice.edu/~rat/index.html External Links: MacTutor · MGP · Wikidata · IdRef Documents Indexed: 82 Publications since 1969, including 2 Books 1 Contribution as Editor Co-Authors: 47 Co-Authors with 61 Joint Publications 957 Co-Co-Authors all top 5 Co-Authors 18 single-authored 20 Zhang, Yin 7 Thompson, James R. 5 Dennis, John E. jun. 5 El-Bakry, Amr S. 4 Byrd, Richard H. 4 Phillips, George N. jun. 3 Martínez, Héctor Jairo 3 Trosset, Michael W. 3 Velázquez, Leticia 2 Argáez, Miguel 2 Gonzaga, Clóvis Caesar 2 González-Lima, María D. 2 Jamrog, Diane C. 2 Papakonstantinou, Joanna M. 2 Potra, Florian-Alexandru 2 Scott, David W. 2 Stoer, Josef 2 Villalobos, Maria Cristina 2 Williams, Pamela J. 2 Ye, Yinyu 1 Celis, M. R. 1 Cocola, Jorio 1 Cores, Debora 1 de Montricher, G. F. 1 El-Alem, Mahmoud M. 1 Fontecilla, Rodrigo 1 Gockenbach, Mark S. 1 Goldstein, Allen A. 1 Gómez, Susana 1 Gragg, William B. 1 Güler, Osman 1 Hennart, Jean-Pierre 1 Kearsley, Anthony José 1 Kearsley, Antony J. 1 Li, Shou-Bai B. 1 McCarthy, Mary Anne 1 McCormick, Garth Philip 1 Melara, Luis A. 1 Parada, Z. 1 Saltzman, Matthew J. 1 Schäfermeyer, Jan P. 1 Steihaug, Trond 1 Symes, William W. 1 Thrall, Robert McDowell 1 Tsuchiya, Takashi 1 Weiser, Alan 1 Whitley, David L. 1 Yabe, Hiroshi 1 Zhang, Yin all top 5 Serials 16 Journal of Optimization Theory and Applications 10 SIAM Journal on Optimization 7 SIAM Journal on Numerical Analysis 5 Mathematical Programming. Series A. Series B 4 SIAM Review 3 American Mathematical Monthly 2 Mathematics of Computation 2 The Annals of Statistics 2 Computational Optimization and Applications 2 Optimization Methods & Software 2 Bulletin of the American Mathematical Society 2 SIAM Journal on Control 1 Inverse Problems 1 Mathematical Programming 1 Numerische Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Annals of Operations Research 1 Computational Statistics 1 Communications in Statistics. Simulation and Computation 1 Linear Algebra and its Applications 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Mathematical Biosciences and Engineering 1 Johns Hopkins Series in the Mathematical Sciences 1 Acta Crystallographica. Section A 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 51 Operations research, mathematical programming (90-XX) 44 Numerical analysis (65-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 10 Statistics (62-XX) 4 Functional analysis (46-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Biology and other natural sciences (92-XX) 2 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Partial differential equations (35-XX) 1 Computer science (68-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 69 Publications have been cited 1,048 times in 824 Documents Cited by ▼ Year ▼ Optimal error bounds for the Newton-Kantorovich theorem. Zbl 0284.65042 Gragg, W. B.; Tapia, R. A. 94 1974 On the formulation and theory of the Newton interior-point method for nonlinear programming. Zbl 0851.90115 El-Bakry, A. S.; Tapia, R. A.; Tsuchiya, T.; Zhang, Y. 85 1996 A trust region strategy for nonlinear equality constrained optimization. Zbl 0566.65048 Celis, M. R.; Dennis, J. E.; Tapia, R. A. 79 1985 Nonparametric probability density estimation. Zbl 0449.62029 Tapia, Richard A.; Thompson, James R. 70 1978 A quadratically convergent \(O(\sqrt n\;L)\)-iteration algorithm for linear programming. Zbl 0778.90037 Ye, Y.; Güler, O.; Tapia, R. A.; Zhang, Y. 49 1993 Diagonalized multiplier methods and quasi-Newton methods for constrained optimization. Zbl 0336.65034 Tapia, R. A. 49 1977 The Kantorovich theorem for Newton’s method. Zbl 0215.27404 Tapia, R. A. 45 1971 Convergence theory for the structured BFGS secant method with an application to nonlinear least squares. Zbl 0645.65026 Dennis, J. E. jun.; Martinez, H. J.; Tapia, R. A. 34 1989 A study of indicators for identifying zero variables in interior-point methods. Zbl 0801.65056 El-Bakry, A. S.; Tapia, R. A.; Zhang, Y. 30 1994 On the superlinear and quadratic convergence of primal-dual interior point linear programming algorithms. Zbl 0763.90066 Zhang, Yin; Tapia, Richard A.; Dennis, John E. jun. 29 1992 A unified approach to global convergence of trust region methods for nonsmooth optimization. Zbl 0835.90086 Dennis, John E. jun.; Li, Shou-Bai B.; Tapia, Richard A. 27 1995 Nonparametric function estimation, modeling and simulation. Zbl 0709.62038 Thompson, James R.; Tapia, Richard A. 26 1990 The gradient projection method under mild differentiability conditions. Zbl 0237.49019 McCormick, G. P.; Tapia, R. A. 23 1972 A convergence theory for a class of quasi-Newton methods for constrained optimization. Zbl 0634.65045 Fontecilla, Rodrigo; Steihaug, Trond; Tapia, Richard A. 23 1987 Nonparametric maximum likelihood estimation of probability densities by penalty function methods. Zbl 0324.62037 de Montricher, G. F.; Tapia, R. A.; Thompson, J. R. 22 1975 Kernel density estimation revisited. Zbl 0363.62030 Scott, David W.; Tapia, Richard A.; Thompson, James R. 20 1977 Quasi-Newton methods for equality constrained optimization: equivalence of existing methods and a new implementation. Zbl 0469.49026 Tapia, R. A. 18 1978 An extension of the Karush-Kuhn-Tucker necessity conditions to infinite programming. Zbl 0805.49014 Tapia, R. A.; Trosset, M. W. 16 1994 The differentiation and integration of nonlinear operators. Zbl 0229.47049 Tapia, R. A. 16 1971 Sizing the BFGS and DFP updates: Numerical study. Zbl 0796.90054 Contreras, M.; Tapia, R. A. 15 1993 An SQP augmented Lagrangian BFGS algorithm for constrained optimization. Zbl 0773.90065 Byrd, R. H.; Tapia, R. A.; Zhang, Yin 15 1992 Superlinear and quadratic convergence of primal-dual interior-point methods for linear programming revisited. Zbl 0792.90078 Zhang, Y.; Tapia, R. A. 13 1992 On secant updates for use in general constrained optimization. Zbl 0657.90088 Tapia, Richard 13 1988 A stable approach to Newton’s method for general mathematical programming problems in R\(^n\). Zbl 0272.65045 Tapia, R. A. 13 1974 The Mehrotra predictor-corrector interior-point method as a perturbated composite Newton method. Zbl 0846.65024 Tapia, R.; Zhang, Y.; Saltzman, M.; Weiser, A. 12 1996 On the superlinear convergence of interior-point algorithms for a general class of problems. Zbl 0781.90074 Zhang, Yin; Tapia, Richard; Potra, Florian 11 1993 Nonparametric probability density estimation by discrete maximum penalized-likelihood criteria. Zbl 0438.62034 Scott, D. W.; Tapia, R. A.; Thompson, J. R. 11 1980 On the global convergence of a modified augmented Lagrangian linesearch interior-point Newton method for nonlinear programming. Zbl 1009.90111 Argáez, M.; Tapia, R. A. 11 2002 Newton’s method for optimization problems with equality constraints. Zbl 0306.90065 Tapia, R. A. 11 1974 A superlinearly convergent polynomial primal-dual interior-point algorithm for linear programming. Zbl 0781.90067 Zhang, Yin; Tapia, Richard A. 10 1993 The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newtons Method. Zbl 0926.92002 Kearsley, Antony J.; Tapia, Richard A.; Trosset, Michael W. 10 1998 On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method. Zbl 0868.90001 González-Lima, María D.; Tapia, Richard A.; Thrall, Robert M. 10 1996 On the characterization of \(Q\)-superlinear convergence of quasi-Newton interior-point methods for nonlinear programming. Zbl 0853.65061 Martinez, H. J.; Parada, Z.; Tapia, R. A. 9 1995 Inverse, shifted inverse, and Rayleigh quotient iteration as Newton’s method. Zbl 1382.65105 Tapia, Richard A.; Dennis, J. E. jun.; Schäfermeyer, Jan P. 9 2018 The metric gradient in normed linear spaces. Zbl 0277.65037 Golomb, M.; Tapia, R. A. 8 1972 A characterization of inner product spaces. Zbl 0286.46025 Tapia, R. A. 8 1973 On the convergence of the Mizuno-Todd-Ye algorithm to the analytic center of the solution set. Zbl 0870.90081 Gonzaga, Clovis C.; Tapia, Richard A. 7 1997 The projected Newton method has order \(1+\sqrt{2}\) for the symmetric eigenvalue problem. Zbl 0674.65012 Tapia, R. A.; Whitley, David L. 6 1988 A fast Newton algorithm for entropy maximization in phase determination. Zbl 0992.65069 Wu, Zhijun; Phillips, George N. jun.; Tapia, Richard; Zhang, Yin 6 2001 Augmented Lagrangian homotopy method for the regularization of total variation denoising problems. Zbl 1124.65058 Melara, L. A.; Kearsley, A. J.; Tapia, R. A. 5 2007 On the role of slack variables in quasi-Newton methods for constrained optimization. Zbl 0457.90070 Tapia, R. A. 5 1980 On effectively computing the analytic center of the solution set by primal-dual interior-point methods. Zbl 0913.65049 González-Lima, María D.; Tapia, Richard A.; Potra, Florian A. 5 1998 On the quadratic convergence of the simplified Mizuno-Todd-Ye algorithm for linear programming. Zbl 0878.65042 Gonzaga, Clovis C.; Tapia, Richard A. 5 1997 A characterization of inner product spaces. Zbl 0271.46014 Tapia, R. A. 5 1973 Newton’s method for problems with equality constraints. Zbl 0244.65036 Tapia, R. A. 4 1974 Computable a posteriori \(L_\infty\)-error bounds for the approximate solution of two-point boundary value problems. Zbl 0315.65047 McCarthy, Mary Anne; Tapia, R. A. 4 1975 Sphere of convergence of Newton’s method on two equivalent systems from nonlinear programming. Zbl 1076.90067 Villalobos, M. C.; Tapia, R. A.; Zhang, Y. 4 2004 Numerical comparisons of path-following strategies for a primal-dual interior-point method for nonlinear programming. Zbl 1026.90095 Argáez, M.; Tapia, R.; Velázquez, L. 4 2002 On the characterization of q-superlinear convergence of quasi-Newton methods for constrained optimization. Zbl 0632.90052 Stoer, J.; Tapia, R. A. 4 1987 On the convergence rate of Newton interior-point methods in the absence of strict complementarity. Zbl 0862.90120 El-Bakry, A. S.; Tapia, R. A.; Zhang, Y. 3 1996 Local behavior of the Newton method on two equivalent systems from linear programming. Zbl 0990.90066 Villalobos, C.; Tapia, R.; Zhang, Y. 3 2002 On sizing and shifting the BFGS update within the sized-Broyden family of secant updates. Zbl 1080.65538 Yabe, H.; Martinez, H. J.; Tapia, R. A. 3 2004 An application of a Newton-like method to the Euler-Lagrange equation. Zbl 0176.41401 Tapia, Richard A. 3 1969 The weak Newton method and boundary value problems. Zbl 0188.22801 Tapia, Richard A. 3 1969 Origin and evolution of the secant method in one dimension. Zbl 1280.01002 Papakonstantinou, Joanna M.; Tapia, Richard A. 3 2013 An optimal-basis identification technique for interior-point linear programming algorithms. Zbl 0737.65052 Tapia, R. A.; Zhang, Yin 3 1991 Perturbation lemma for the Newton method with application to the SQP Newton method. Zbl 0907.90217 Cores, D.; Tapia, R. A. 2 1998 An approach to parallelizing isotonic regression. Zbl 0906.65147 Kearsley, Anthony J.; Tapia, Richard A.; Trosset, Michael W. 2 1996 On convergence of minimization methods: Attraction, repulsion, and selection. Zbl 0969.90084 Zhang, Y.; Tapia, R.; Velázquez, L. 2 2000 A general approach to Newton’s method for Banach space problems with equality constraints. Zbl 0297.47056 Tapia, R. A. 2 1974 An extension of Curry’s theorem to steepest descent in normed linear spaces. Zbl 0317.90048 Byrd, R. H.; Tapia, R. A. 2 1975 Numerical experience with a polyhedral-norm CDT trust-region algorithm. Zbl 0831.90103 El-Alem, M. M.; Tapia, R. A. 2 1995 Nonparametric density estimation: Where do we go from here? Zbl 0448.62024 Tapia, R. A.; Thompson, J. R. 1 1979 Selective search for global optimization of zero or small residual least-squares problems: A numerical study. Zbl 0990.90109 Velázquez, L.; Phillips, G. N. jun.; Tapia, R. A.; Zhang, Y. 1 2001 Kantorovich estimates for some convex programs. Zbl 0285.49002 Goldstein, A. A.; Tapia, R. A. 1 1973 Hamel versus Schauder dimension. Zbl 0189.42902 Evans, J. W.; Tapia, R. A. 1 1970 On averaging and representation properties of the BFGS and related secant updates. Zbl 1328.49028 Tapia, Richard 1 2015 A fast Newton method for entropy maximization in statistical phase estimation. Zbl 1370.82040 Wu, Zhijun; Phillips, George N. jun.; Tapia, Richard; Zhang, Yin 1 2001 Generation of classes of symmetric rank-2 secant updates and the maximality of the Davidon class. Zbl 1308.65077 Papakonstantinou, Joanna M.; Tapia, Richard A. 1 2012 Inverse, shifted inverse, and Rayleigh quotient iteration as Newton’s method. Zbl 1382.65105 Tapia, Richard A.; Dennis, J. E. jun.; Schäfermeyer, Jan P. 9 2018 On averaging and representation properties of the BFGS and related secant updates. Zbl 1328.49028 Tapia, Richard 1 2015 Origin and evolution of the secant method in one dimension. Zbl 1280.01002 Papakonstantinou, Joanna M.; Tapia, Richard A. 3 2013 Generation of classes of symmetric rank-2 secant updates and the maximality of the Davidon class. Zbl 1308.65077 Papakonstantinou, Joanna M.; Tapia, Richard A. 1 2012 Augmented Lagrangian homotopy method for the regularization of total variation denoising problems. Zbl 1124.65058 Melara, L. A.; Kearsley, A. J.; Tapia, R. A. 5 2007 Sphere of convergence of Newton’s method on two equivalent systems from nonlinear programming. Zbl 1076.90067 Villalobos, M. C.; Tapia, R. A.; Zhang, Y. 4 2004 On sizing and shifting the BFGS update within the sized-Broyden family of secant updates. Zbl 1080.65538 Yabe, H.; Martinez, H. J.; Tapia, R. A. 3 2004 On the global convergence of a modified augmented Lagrangian linesearch interior-point Newton method for nonlinear programming. Zbl 1009.90111 Argáez, M.; Tapia, R. A. 11 2002 Numerical comparisons of path-following strategies for a primal-dual interior-point method for nonlinear programming. Zbl 1026.90095 Argáez, M.; Tapia, R.; Velázquez, L. 4 2002 Local behavior of the Newton method on two equivalent systems from linear programming. Zbl 0990.90066 Villalobos, C.; Tapia, R.; Zhang, Y. 3 2002 A fast Newton algorithm for entropy maximization in phase determination. Zbl 0992.65069 Wu, Zhijun; Phillips, George N. jun.; Tapia, Richard; Zhang, Yin 6 2001 Selective search for global optimization of zero or small residual least-squares problems: A numerical study. Zbl 0990.90109 Velázquez, L.; Phillips, G. N. jun.; Tapia, R. A.; Zhang, Y. 1 2001 A fast Newton method for entropy maximization in statistical phase estimation. Zbl 1370.82040 Wu, Zhijun; Phillips, George N. jun.; Tapia, Richard; Zhang, Yin 1 2001 On convergence of minimization methods: Attraction, repulsion, and selection. Zbl 0969.90084 Zhang, Y.; Tapia, R.; Velázquez, L. 2 2000 The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newtons Method. Zbl 0926.92002 Kearsley, Antony J.; Tapia, Richard A.; Trosset, Michael W. 10 1998 On effectively computing the analytic center of the solution set by primal-dual interior-point methods. Zbl 0913.65049 González-Lima, María D.; Tapia, Richard A.; Potra, Florian A. 5 1998 Perturbation lemma for the Newton method with application to the SQP Newton method. Zbl 0907.90217 Cores, D.; Tapia, R. A. 2 1998 On the convergence of the Mizuno-Todd-Ye algorithm to the analytic center of the solution set. Zbl 0870.90081 Gonzaga, Clovis C.; Tapia, Richard A. 7 1997 On the quadratic convergence of the simplified Mizuno-Todd-Ye algorithm for linear programming. Zbl 0878.65042 Gonzaga, Clovis C.; Tapia, Richard A. 5 1997 On the formulation and theory of the Newton interior-point method for nonlinear programming. Zbl 0851.90115 El-Bakry, A. S.; Tapia, R. A.; Tsuchiya, T.; Zhang, Y. 85 1996 The Mehrotra predictor-corrector interior-point method as a perturbated composite Newton method. Zbl 0846.65024 Tapia, R.; Zhang, Y.; Saltzman, M.; Weiser, A. 12 1996 On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method. Zbl 0868.90001 González-Lima, María D.; Tapia, Richard A.; Thrall, Robert M. 10 1996 On the convergence rate of Newton interior-point methods in the absence of strict complementarity. Zbl 0862.90120 El-Bakry, A. S.; Tapia, R. A.; Zhang, Y. 3 1996 An approach to parallelizing isotonic regression. Zbl 0906.65147 Kearsley, Anthony J.; Tapia, Richard A.; Trosset, Michael W. 2 1996 A unified approach to global convergence of trust region methods for nonsmooth optimization. Zbl 0835.90086 Dennis, John E. jun.; Li, Shou-Bai B.; Tapia, Richard A. 27 1995 On the characterization of \(Q\)-superlinear convergence of quasi-Newton interior-point methods for nonlinear programming. Zbl 0853.65061 Martinez, H. J.; Parada, Z.; Tapia, R. A. 9 1995 Numerical experience with a polyhedral-norm CDT trust-region algorithm. Zbl 0831.90103 El-Alem, M. M.; Tapia, R. A. 2 1995 A study of indicators for identifying zero variables in interior-point methods. Zbl 0801.65056 El-Bakry, A. S.; Tapia, R. A.; Zhang, Y. 30 1994 An extension of the Karush-Kuhn-Tucker necessity conditions to infinite programming. Zbl 0805.49014 Tapia, R. A.; Trosset, M. W. 16 1994 A quadratically convergent \(O(\sqrt n\;L)\)-iteration algorithm for linear programming. Zbl 0778.90037 Ye, Y.; Güler, O.; Tapia, R. A.; Zhang, Y. 49 1993 Sizing the BFGS and DFP updates: Numerical study. Zbl 0796.90054 Contreras, M.; Tapia, R. A. 15 1993 On the superlinear convergence of interior-point algorithms for a general class of problems. Zbl 0781.90074 Zhang, Yin; Tapia, Richard; Potra, Florian 11 1993 A superlinearly convergent polynomial primal-dual interior-point algorithm for linear programming. Zbl 0781.90067 Zhang, Yin; Tapia, Richard A. 10 1993 On the superlinear and quadratic convergence of primal-dual interior point linear programming algorithms. Zbl 0763.90066 Zhang, Yin; Tapia, Richard A.; Dennis, John E. jun. 29 1992 An SQP augmented Lagrangian BFGS algorithm for constrained optimization. Zbl 0773.90065 Byrd, R. H.; Tapia, R. A.; Zhang, Yin 15 1992 Superlinear and quadratic convergence of primal-dual interior-point methods for linear programming revisited. Zbl 0792.90078 Zhang, Y.; Tapia, R. A. 13 1992 An optimal-basis identification technique for interior-point linear programming algorithms. Zbl 0737.65052 Tapia, R. A.; Zhang, Yin 3 1991 Nonparametric function estimation, modeling and simulation. Zbl 0709.62038 Thompson, James R.; Tapia, Richard A. 26 1990 Convergence theory for the structured BFGS secant method with an application to nonlinear least squares. Zbl 0645.65026 Dennis, J. E. jun.; Martinez, H. J.; Tapia, R. A. 34 1989 On secant updates for use in general constrained optimization. Zbl 0657.90088 Tapia, Richard 13 1988 The projected Newton method has order \(1+\sqrt{2}\) for the symmetric eigenvalue problem. Zbl 0674.65012 Tapia, R. A.; Whitley, David L. 6 1988 A convergence theory for a class of quasi-Newton methods for constrained optimization. Zbl 0634.65045 Fontecilla, Rodrigo; Steihaug, Trond; Tapia, Richard A. 23 1987 On the characterization of q-superlinear convergence of quasi-Newton methods for constrained optimization. Zbl 0632.90052 Stoer, J.; Tapia, R. A. 4 1987 A trust region strategy for nonlinear equality constrained optimization. Zbl 0566.65048 Celis, M. R.; Dennis, J. E.; Tapia, R. A. 79 1985 Nonparametric probability density estimation by discrete maximum penalized-likelihood criteria. Zbl 0438.62034 Scott, D. W.; Tapia, R. A.; Thompson, J. R. 11 1980 On the role of slack variables in quasi-Newton methods for constrained optimization. Zbl 0457.90070 Tapia, R. A. 5 1980 Nonparametric density estimation: Where do we go from here? Zbl 0448.62024 Tapia, R. A.; Thompson, J. R. 1 1979 Nonparametric probability density estimation. Zbl 0449.62029 Tapia, Richard A.; Thompson, James R. 70 1978 Quasi-Newton methods for equality constrained optimization: equivalence of existing methods and a new implementation. Zbl 0469.49026 Tapia, R. A. 18 1978 Diagonalized multiplier methods and quasi-Newton methods for constrained optimization. Zbl 0336.65034 Tapia, R. A. 49 1977 Kernel density estimation revisited. Zbl 0363.62030 Scott, David W.; Tapia, Richard A.; Thompson, James R. 20 1977 Nonparametric maximum likelihood estimation of probability densities by penalty function methods. Zbl 0324.62037 de Montricher, G. F.; Tapia, R. A.; Thompson, J. R. 22 1975 Computable a posteriori \(L_\infty\)-error bounds for the approximate solution of two-point boundary value problems. Zbl 0315.65047 McCarthy, Mary Anne; Tapia, R. A. 4 1975 An extension of Curry’s theorem to steepest descent in normed linear spaces. Zbl 0317.90048 Byrd, R. H.; Tapia, R. A. 2 1975 Optimal error bounds for the Newton-Kantorovich theorem. Zbl 0284.65042 Gragg, W. B.; Tapia, R. A. 94 1974 A stable approach to Newton’s method for general mathematical programming problems in R\(^n\). Zbl 0272.65045 Tapia, R. A. 13 1974 Newton’s method for optimization problems with equality constraints. Zbl 0306.90065 Tapia, R. A. 11 1974 Newton’s method for problems with equality constraints. Zbl 0244.65036 Tapia, R. A. 4 1974 A general approach to Newton’s method for Banach space problems with equality constraints. Zbl 0297.47056 Tapia, R. A. 2 1974 A characterization of inner product spaces. Zbl 0286.46025 Tapia, R. A. 8 1973 A characterization of inner product spaces. Zbl 0271.46014 Tapia, R. A. 5 1973 Kantorovich estimates for some convex programs. Zbl 0285.49002 Goldstein, A. A.; Tapia, R. A. 1 1973 The gradient projection method under mild differentiability conditions. Zbl 0237.49019 McCormick, G. P.; Tapia, R. A. 23 1972 The metric gradient in normed linear spaces. Zbl 0277.65037 Golomb, M.; Tapia, R. A. 8 1972 The Kantorovich theorem for Newton’s method. Zbl 0215.27404 Tapia, R. A. 45 1971 The differentiation and integration of nonlinear operators. Zbl 0229.47049 Tapia, R. A. 16 1971 Hamel versus Schauder dimension. Zbl 0189.42902 Evans, J. W.; Tapia, R. A. 1 1970 An application of a Newton-like method to the Euler-Lagrange equation. Zbl 0176.41401 Tapia, Richard A. 3 1969 The weak Newton method and boundary value problems. Zbl 0188.22801 Tapia, Richard A. 3 1969 all cited Publications top 5 cited Publications all top 5 Cited by 1,116 Authors 30 Argyros, Ioannis Konstantinos 24 Tapia, Richard A. 13 Potra, Florian-Alexandru 13 Zhang, Yin 12 Yamamoto, Tetsuro 11 Bouzebda, Salim 11 Ye, Yinyu 10 Zhu, Detong 9 Hilout, Saïd 8 González-Lima, María D. 8 Martínez, José Mario 8 Yuan, Ya-xiang 7 Sun, Jie 7 Xia, Yong 6 Byrd, Richard H. 6 Li, Chong 6 Magreñán, Ángel Alberto 6 Orban, Dominique 6 Ruggiero, Valeria 6 Zhao, Gongyun 5 Bonettini, Silvia 5 Cătinaş, Emil 5 El-Alem, Mahmoud M. 5 Ma, Changfeng 5 Mahdavi-Amiri, Nezam 5 Qi, Liqun 5 Slaoui, Yousri 5 Wang, Jiulin 5 Yabe, Hiroshi 4 Andreani, Roberto 4 Armand, Paul 4 Burer, Samuel 4 Durazzi, Carla 4 Engau, Alexander 4 Galligani, Emanuele 4 Güler, Osman 4 Hager, William W. 4 Jian, Jinbao 4 Mitchell, John E. 4 Petra, Cosmin G. 4 Pillonetto, Gianluigi 4 Roos, Cornelis 4 Rückmann, Jan-Joachim 4 Rustem, Berc 4 Sim, Chee-Khian 4 Thrall, Robert McDowell 4 Uko, Livinus Ugochukwu 4 Wächter, Andreas 4 Wei, Zengxin 3 Abramov, Rafail V. 3 Ai, Wenbao 3 Al-Baali, Mehiddin 3 Anjos, Miguel F. 3 Babaie-Kafaki, Saman 3 Benoist, Joël 3 Beynon, Malcolm James 3 Caboussat, Alexandre 3 Chen, Dong 3 Didi, Sultana 3 El-Bakry, Amr S. 3 El-Sobky, Bothina 3 Facchinei, Francisco 3 Gill, Philip E. 3 Gondzio, Jacek 3 Guerra Vázquez, Francisco 3 Hernández, Miguel Ángel 3 Huang, Zhengda 3 Jarre, Florian 3 Jerome, Joseph W. 3 Kelley, Carl T. 3 Liu, Hongwei 3 Liu, Xinwei 3 Locatelli, Marco 3 Mehrotra, Sanjay 3 Melara, Luis A. 3 Miel, George J. 3 Mizuno, Shinji 3 Moré, Jorge J. 3 Murray, Walter 3 Ng, Kung-Fu 3 Nocedal, Jorge 3 Puri, Madan Lal 3 Redner, Richard A. 3 Robinson, Daniel P. 3 Sachs, Ekkehard W. 3 Salahi, Maziar 3 Santos, Sandra Augusta 3 Sicilia, Juan Antonio 3 Simon, Jaan-Willem 3 Spedicato, Emilio 3 Terlaky, Tamás 3 Tsuchiya, Takashi 3 Tunçel, Levent 3 Wang, Jinhua 3 Wang, Qiuping 3 Weichert, Dieter 3 Wright, Stephen J. 3 Wu, Zhijun 3 Yamashita, Hiroshi 3 Yan, Ting ...and 1,016 more Authors all top 5 Cited in 186 Serials 94 Journal of Optimization Theory and Applications 70 Mathematical Programming. Series A. Series B 36 Journal of Computational and Applied Mathematics 34 Computational Optimization and Applications 32 Applied Mathematics and Computation 23 SIAM Journal on Optimization 21 Optimization 19 Numerical Algorithms 19 Optimization Methods & Software 17 Communications in Statistics. Theory and Methods 15 Computational Statistics and Data Analysis 14 European Journal of Operational Research 13 Journal of Mathematical Analysis and Applications 12 Annals of Operations Research 11 Journal of Global Optimization 10 Mathematical Programming 9 Journal of Statistical Planning and Inference 9 International Journal of Computer Mathematics 8 Annals of the Institute of Statistical Mathematics 8 Computing 8 Applied Numerical Mathematics 7 Computers & Mathematics with Applications 7 Journal of Computational Physics 7 Numerische Mathematik 7 Statistics & Probability Letters 7 Computational and Applied Mathematics 6 Journal of Multivariate Analysis 6 Journal of Nonparametric Statistics 6 Optimization Letters 5 Mathematics of Computation 5 Automatica 5 Numerical Functional Analysis and Optimization 5 Japan Journal of Applied Mathematics 5 Journal of Complexity 5 Applied Mathematics Letters 5 Journal of Industrial and Management Optimization 4 The Canadian Journal of Statistics 4 The Annals of Statistics 4 Operations Research Letters 4 Acta Mathematicae Applicatae Sinica. English Series 4 Computers & Operations Research 4 Computational Statistics 4 Journal of Statistical Computation and Simulation 4 Linear Algebra and its Applications 4 Mathematical Methods of Operations Research 4 Optimization and Engineering 4 Science China. Mathematics 3 Mathematical Biosciences 3 Journal of Econometrics 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Proceedings of the American Mathematical Society 3 Journal of Symbolic Computation 3 Mathematical and Computer Modelling 3 Communications in Statistics. Simulation and Computation 3 SIAM Review 3 Top 3 Journal of Inequalities and Applications 3 Acta Mathematica Sinica. English Series 3 Journal of Systems Science and Complexity 3 Journal of Applied Mathematics and Computing 3 Mathematical Programming Computation 2 Computer Methods in Applied Mechanics and Engineering 2 Computer Physics Communications 2 Metrika 2 Periodica Mathematica Hungarica 2 Applied Mathematics and Optimization 2 Calcolo 2 International Journal for Numerical Methods in Engineering 2 Journal of Approximation Theory 2 Mathematics and Computers in Simulation 2 SIAM Journal on Numerical Analysis 2 Statistica Neerlandica 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Optimal Control Applications & Methods 2 Revue de Statistique Appliquée 2 Journal of Computational Mathematics 2 Probability Theory and Related Fields 2 Journal of Scientific Computing 2 Aequationes Mathematicae 2 Applied Mathematical Modelling 2 International Journal of Robust and Nonlinear Control 2 SIAM Journal on Scientific Computing 2 Statistical Papers 2 Journal of Convex Analysis 2 Journal of Mathematical Chemistry 2 The Econometrics Journal 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Statistical Methods and Applications 2 Bulletin of the American Mathematical Society 2 Set-Valued and Variational Analysis 2 Sankhyā. Series A 2 Statistics and Computing 1 Applicable Analysis 1 International Journal of Engineering Science 1 Inverse Problems 1 Journal of the Franklin Institute 1 Rocky Mountain Journal of Mathematics 1 Scandinavian Journal of Statistics 1 Bulletin of Mathematical Biology 1 Acta Mathematica Vietnamica ...and 86 more Serials all top 5 Cited in 41 Fields 481 Operations research, mathematical programming (90-XX) 344 Numerical analysis (65-XX) 142 Statistics (62-XX) 129 Calculus of variations and optimal control; optimization (49-XX) 75 Operator theory (47-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Probability theory and stochastic processes (60-XX) 19 Computer science (68-XX) 18 Systems theory; control (93-XX) 15 Partial differential equations (35-XX) 15 Functional analysis (46-XX) 11 Mechanics of deformable solids (74-XX) 9 Biology and other natural sciences (92-XX) 8 Real functions (26-XX) 8 Ordinary differential equations (34-XX) 8 Geophysics (86-XX) 8 Information and communication theory, circuits (94-XX) 7 Approximations and expansions (41-XX) 7 Integral equations (45-XX) 7 Fluid mechanics (76-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Convex and discrete geometry (52-XX) 4 Optics, electromagnetic theory (78-XX) 3 Measure and integration (28-XX) 3 Functions of a complex variable (30-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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