Richard A. Tapia | Academic Influence

Richard A. Tapia's AcademicInfluence.com Rankings

Richard A. Tapia

Mathematics

#2604

World Rank

#3992

Historical Rank

#1019

USA Rank

Measure Theory

#2475

World Rank

#2975

Historical Rank

#700

USA Rank

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Mathematics

Richard A. Tapia's Degrees

Bachelors Mathematics University of Texas at Austin

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According to Wikipedia, Richard Alfred Tapia is an American mathematician and University Professor at Rice University in Houston, Texas, the university's highest academic title. In 2011, President Obama awarded Tapia the National Medal of Science. He is currently the Maxfield and Oshman Professor of Engineering; Associate Director of Graduate Studies, Office of Research and Graduate Studies; and Director of the Center for Excellence and Equity in Education at Rice University.

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Richard A. Tapia's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

On the formulation and theory of the Newton interior-point method for nonlinear programming (1996) (397)
Nonparametric Probability Density Estimation (1978) (329)
A trust region strategy for nonlinear equality constrained op-timization (1984) (234)
Optimal Error Bounds for the Newton–Kantorovich Theorem (1974) (173)
Diagonalized multiplier methods and quasi-Newton methods for constrained optimization (1977) (170)
Quantification of regional ventilation from treatment planning CT. (2005) (156)
Nonparametric Function Estimation, Modeling, and Simulation (1987) (150)
The Kantorovich Theorem for Newton's Method (1971) (119)
A quadratically convergent O( $$\sqrt n $$ L)-iteration algorithm for linear programming (1993) (118)
Nonparametric Maximum Likelihood Estimation of Probability Densities by Penalty Function Methods (1975) (107)
A Study of Indicators for Identifying Zero Variables in Interior-Point Methods (1994) (99)
On the Superlinear and Quadratic Convergence of Primal-Dual Interior Point Linear Programming Algorithms (1992) (96)
Kernel density estimation revisited (1977) (94)
The Gradient Projection Method under Mild Differentiability Conditions (1972) (84)
Convergence theory for the structured BFGS secant method with an application to nonlinear least squares (1989) (83)
The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method (1995) (80)
A unified approach to global convergence of trust region methods for nonsmooth optimization (1995) (62)
QUASI-NEWTON METHODS FOR EQUALITY CONSTRAINED OPTIMIZATION: EQUIVALENCE OF EXISTING METHODS AND A NEW IMPLEMENTATION (1978) (60)
Nonparametric Probability Density Estimation by Discrete Maximum Penalized- Likelihood Criteria (1980) (57)
Science and Engineering Indicators 2000. Volume 1 (2000) (55)
An SQP Augmented Lagrangian BFGS Algorithm for Constrained Optimization (1992) (54)
On secant updates for use in general constrained optimization (1988) (51)
A Convergence Theory for a Class of Quasi-Newton Methods for Constrained Optimization (1987) (51)
On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming (2002) (44)
Role of slack variables in quasi-Newton methods for constrained optimization (1979) (42)
On the Superlinear Convergence of Interior-Point Algorithms for a General Class of Problems (1993) (41)
Practical Methods of Optimization, Volume 2: Constrained Optimization (R. Fletcher) (1984) (41)
Superlinear and quadratic convergence of primal-dual interior-point methods for linear programming revisited (1992) (37)
A global convergence theory for a class of trust region algorithms for constrained optimization (1988) (36)
The Differentiation and Integration of Nonlinear Operators (1971) (35)
A stable approach to Newton's method for general mathematical programming problems inRn (1975) (31)
An Extension of the Karush-Kuhn-Tucker Necessity Conditions to Infinite Programming (1994) (30)
An Optimal Basis Identification Technique for Interior-Point Linear Programming Algorithms (1991) (30)
The Mehrotra Predictor-Corrector Interior-Point Method As a Perturbed Composite Newton Method (1996) (29)
Sizing the BFGS and DFP updates: Numerical study (1993) (29)
A Trust Region Strategy for Equality Constrained Optimization (1984) (28)
A Global Convergence Theory for Arbitrary Norm Trust-Region Methods for Nonlinear Equations (1995) (28)
On the Convergence of the Mizuno-Todd-Ye Algorithm to the Analytic Center of the Solution Set (1997) (27)
A Fast Newton Algorithm for Entropy Maximization in Phase Determination (2001) (27)
Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton's Method (2018) (26)
Newton’s Method for Optimization Problems with Equality Constraints (1974) (26)
A Superlinearly Convergent Polynomial Primal-Dual Interior-Point Algorithm for Linear Programming (1993) (26)
Chapter 6 On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method (1996) (24)
A characterization of inner product spaces (1973) (24)
The dual regularization approach to seismic velocity inversion (1995) (22)
Numerical Comparisons of Path-Following Strategies for a Primal-Dual Interior-Point Method for Nonlinear Programming (2002) (20)
On the convergence rate of Newton interior-point methods in the absence of strict complementarity (1996) (19)
The Projected Newton Method Has Order $1 + \sqrt 2 $ for the Symmetric Eigenvalue Problem (1988) (18)
On the characterization of Q-superlinear convergence of quasi-Newton interior-point methods for nonlinear programming (1995) (17)
On Effectively Computing the Analytic Center of the Solution Set by Primal-Dual Interior-Point Methods (1998) (16)
QDN: a variable storage algorithm for unconstrained optimization (1978) (15)
On the Formulation of the Primal-Dual Newton Interior-Point Method for Nonlinear Programming (1992) (15)
Origin and Evolution of the Secant Method in One Dimension (2013) (15)
The metric gradient in normed linear spaces (1972) (15)
On the Characterization of Q-superlinear Convergence of Quasi-Newton Methods for Constrained Optimization (1987) (14)
On the convergence of the iteration sequence in primal-dual interior-point methods (1995) (13)
THE KANTOROVICH THEOREM AND ERROR ESTIMATES FOR NEWTON'S METHOD. (1970) (13)
Newton's Method for Problems with Equality Constraints (1974) (13)
Computable a Posteriori $L_\infty $-Error Bounds for the Approximate Solution of Two-Point Boundary Value Problems (1975) (12)
An Interior-point Method with Polynomial Complexity and Superlinear Convergence for Linear Complementarity Problems (1991) (12)
On Convergence of Minimization Methods: Attraction, Repulsion, and Selection (2000) (12)
A Superlinearly Convergent O( P Nl)-iteration Algorithm for Linear Programming (1991) (11)
Advances in Numerical Partial Differential Equations and Optimization: Proceedings of the Fifth Mexico-United States Workshop (1991) (11)
On Sizing and Shifting the BFGS Update within the Sized-Broyden Family of Secant Updates (2004) (10)
Underrepresented Minority Achievement and Course Taking: The Kindergarten-Graduate Continuum. (2000) (10)
A nonlinear model for top fuel dragster dynamic performance assessment (2008) (10)
Hiring and developing minority faculty at research universities (2010) (9)
On the Quadratic Convergence of the Simplified Mizuno-Todd-Ye Algorithm for Linear Programming (1997) (9)
True Diversity Doesn't Come from Abroad. (2007) (9)
A Random Number Generator for Continuous Random Variables Based on an Interpolation Procedure of Akima (1970) (8)
Augmented Lagrangian Homotopy Method for the Regularization of Total Variation Denoising Problems (2007) (8)
Mathematical ship lofting (1962) (8)
On the Convergence of Interior-Point Methods to the Center of the Solution Set in Linear Programming (1991) (8)
An Approach to Parallelizing Isotonic Regression (1996) (8)
Numerical experience with a polyhedral-norm CDT trust-region algorithm (1995) (7)
Selective Search for Global Optimization of Zero or Small Residual Least-Squares Problems: A Numerical Study (2001) (7)
An Inexact Trust-Region Feasible-Point Algorithm for Nonlinear Systems of Equalities and Inequalitie (1995) (7)
Perturbation Lemma for the Newton Method with Application to the SQP Newton Method (1998) (7)
A stable approach to Newton's method for general mathematical programming problems inRn (1974) (7)
An extension of Curry's theorem to steepest descent in normed linear spaces (1975) (7)
Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming (2004) (6)
The Weak Newton Method and Boundary Value Problems (1969) (6)
Approximation of Solutions for Location Problems (5)
An application of a Newton-like method to the Euler-Lagrange equation. (1969) (5)
Promoting National Minority Leadership in Science and Engineering: A Report on Proposed Actions. (2000) (5)
The Isoperimetric Problem Revisited : Extracting a Short Proof of Sufficiency from Euler ’ s 1744 Approach to Necessity ∗ (2013) (4)
On the Fundamental Role of Interior-point Methodology in Constrained Optimization on the Fundamental Role of Interior-point Methodology in Constrained Optimization 1 (1997) (4)
Convergence Rates for the Variable, the Multiplier, and the Pair in SQP Methods (1989) (4)
A Superlinearly Convergent O(square root of nL)-Iteration Algorithm for Linear Programming (1991) (4)
Karmarkar as a Classical Method (1987) (4)
Effective computation of the analytic center of the solution set in linear programming using primal-dual interior-point methods (1995) (4)
On averaging and representation properties of the BFGS and related secant updates (2015) (4)
An Extremum Problem (1972) (3)
Research on trust-region algorithms for nonlinear programming (1991) (3)
MULTIVARIATE DENSITY ESTIMATION BY DISCRETE MAXIMUM PENALIZED LIKELIHOOD METHODS (1978) (3)
A Local Procedure for Error Detection and Data Smoothing. (1974) (3)
Kantorovich Estimates for Some Convex Programs (1973) (3)
Cubically convergent method for locating a nearby vertex in linear programming (1990) (3)
A Quasi-Discrete Newton Algorithm with a Nonmonotone Stabilization Technique (3)
On the Quadratic Convergence of the Singular Newton's Method (1992) (3)
Augmented Lagrangian methods for constrained optimization: the role of the penalty constant (1979) (3)
Nonparametric Bayesian Estimation of Probability Densities by Function Space Techniques (1973) (2)
Comparison of Two Sets of First-Order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds (2002) (2)
Engineering Optimization: Methods and Applications (G. V. Reklaitis, A. Ravindran and K. M. Ragsdell) (1986) (2)
The Bayesian Statistical Approach to the Phase Problem in Protein X-ray Crystallography (1999) (2)
An Algorithm for Nonparametric Density Estimation (1976) (2)
Simultaneous Structure Factor and Contrast Transfer Function Parameter Determination in Transmission (2000) (2)
Generation of classes of symmetric rank-2 secant updates and the maximality of the Davidon class (2012) (2)
Hamel Versus Schauder Dimension (1970) (2)
Supplementary terminology for nonlinear iterative methods (1976) (2)
Optimal smoothing of direct estimates of the power spectrum (1978) (2)
A general approach to Newton’s method for Banach space problems with equality constraints (1974) (2)
The Behavior of Newton-Type Methods on Two Equivalent Systems from Linear Programming (1998) (1)
Data smoothing and error detection based on linear interpolation (1972) (1)
Computational Experience of an Augmented Lagrangian for Nonlinear Programming as a Merit Function in a Primal-Dual Interior-Point Method (1995) (1)
A global optimization method for the molecular replacement problem in X-ray crystallography (2005) (1)
Extending the Farkas Lemma Approach to Necessity Conditions to Infinite Programming (1993) (1)
7. Nonparametric Regression and Intensity Function Estimation (1990) (1)
Examining the effectiveness of teacher training on the improvement of California standardized test scores at Eva B. Elementary School (2008) (1)
2. Some Approaches to Nonparametric Density Estimation (1990) (1)
Numerical Optimization At the Center for Research On Parallel Computation (1994) (1)
Using Indicators in Finite Termination Procedures (1999) (1)
8. Model Building: Speculative Data Analysis (1990) (1)
The Effect of the Separation of Variables on the Molecular Replacement Method (2000) (1)
3. Maximum Likelihood Density Estimation (1990) (0)
A geometrical interpretation of the 2n-th central difference (1972) (0)
A random number generator for continuous random variables (1972) (0)
EQUIVALENCE OF CONJUGATE GRADIENT METHODS AND QUASI-NEWTON METHODS (1979) (0)
Parallel Structured Optimization Algorithms for Inverse Problems (1993) (0)
4. Maximum Penalized Likelihood Estimation (1990) (0)
A Robust Choice of the Lagrange Multiplier in the SQP Newton Method (1994) (0)
Research on trust-region algorithms for nonlinear programming. Final technical report, 1 January 1990--31 December 1992 (1995) (0)
The Gradient Projection Method and Curry's Theorem. (1970) (0)
A UNIFIED APPROACH TO MATHEMATICAL OPTIMIZATION AND LAGRANGE MULTIPLIER THEORY FOR SCIENTISTS AND ENGINEERS (2011) (0)
The Projected Newton Method Has Order 1 + Square Root of 2 for the Symmetric Eigenvalue Problem (1987) (0)
5. Discrete Maximum Penalized Likelihood Estimation (1990) (0)
Committee on Nominations (1999) (0)
Keynote lecture 4: if it's fast it must be Newton's method (2009) (0)
On the Convergence of the Tapia Indicators in the Absence of Strict Complementarity (1993) (0)
On the use of indicator functions for identifying binding constrants in constrained optimization problems (1994) (0)
6. Nonparametric Density Estimation in Higher Dimensions (1990) (0)
Selected Activities From Exemplary Learning Plans Multiplication (2 nd Grade) (2015) (0)
Quasi-Newton methods for large scale nonlinear equations and constrained optimization: Progress report, July 1, 1987-June 30, 1988 (1988) (0)
Research in Constrained Optimization (1989) (0)
Some Issues in Nonlinear Programming Algorithms for Problems with Simulation Constraints. (1995) (0)
Logarithmic Indicators and the Identification of Subgroups of Variables in Interior-Point Methods (1993) (0)
On effectively computing the analytic center by primal-dual interior point methods (1994) (0)
The E ect of the Separation of Variables onthe Molecular Replacement (2000) (0)
1. Historical Background (1990) (0)
KRYLOV-ORTHOGONAL PROJECTION METHOD FOR NONLINEAR PROGRAMMING (2004) (0)
A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming] (1976) (0)
TU-EE-A3-06: Sub-Millimeter Three Dimensional Ventilation Imaging of Rodent Lungs (2005) (0)
Integrated Approaches to Parallelism in Optimization and the Solution of Inverse Problems (1992) (0)
On averaging and representation properties of the BFGS and related secant updates (2014) (0)
Final Report of Robert M. Thrall and Associates to U. S. Army Strategy and Tactics Analysis Group. (STAG). (1972) (0)
Distance-parametrized Optimization Methods for Structural Molecular Biology 1 Introduction (0)
RICE UNIVERSITY Historical Development of the BFGS Secant Method and Its Characterization Properties (2009) (0)
Karl Pearson was Right (1978) (0)
Convergence of the Gradient Method in Normed Linear Spaces. (1974) (0)
Generalized Fractional Programming: Optimality and Duality Theory' (2004) (0)
SCHAUDER DIMENSION IN BANACH SPACES. (1968) (0)
Advanced Problems: 5826-5831 (1971) (0)
Research on trust-region algorithms for nonlinear programming. Progress report, January 1, 1991--December 31, 1991 (1991) (0)
Seismic velocity inversion by differential semblance optimization (1994) (0)
On the Generation of Updates for Quasi-Newton Methods ' (0)
Richard Tapia (2021) (0)
Part I: Overview and Management (2004) (0)
Making It in Engineering : The Career Attainment and Mobility of Caucasian , Black , and Asian-American Engineers (2000) (0)
Science and Engineering Indicators 2000. Volume 2: Appendix Tables (2000) (0)
My reflections on the Blackwell-Tapia Prize. (2013) (0)
4th Annual Conference for African-American Researchers in the Mathematical Sciences (CAARMS4). Preliminary Program (1998) (0)
Reinventing the International Human Rights Regime: Evolution and Effectiveness of the UN Human Rights Council (2016) (0)
Extending the Pennisi-McCormick Second-Order Sufficiency Theory for Nonlinear Programming to Infinite Dimensions (2019) (0)

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