An Introduction to Mathematical Optimization Theory, Jones and Bartlett, in preparation.
Nonparametric Function Estimation, Modeling, and Simulation, SIAM, Philadelphia, Pennsylvania, 1990. A revision of Nonparametric Density Estimation (with J.R. Thompson).
Nonparametric Density Estimation, Johns Hopkins University Press, Baltimore, Maryland, 1978 (with J.R. Thompson).
Papers
Mathematical Ship lofting, Journal of Ship Research, 10 (1966), 203-222 (with S. Berger, W. Webster, and D. Atkins).
An Application of a Newton-like Method to the Euler-Lagrange Equation, Pacific Journal of Mathematics, 29(1969), 235-245.
The Weak Newton Method and Boundary Value Problems, SIAM Journal on Numerical Analysis, 6 (1969), 539-550.
Hamel versus Schauder Dimension, American Mathematical Monthly, 77 (1970), 385- 388 (with J.W. Evans).
The Kantorovich Theorem for Newton's Method, American Mathematical Monthly, 78 (1971), 389-392.
The Differentiation and Integration of Nonlinear Operators, Nonlinear Functional Analysis and Applications, (1971), (ed. L.B. Rall) Academic Press, New York, 45-101.
The Gradient Projection Method under Mild Differentiability Conditions, SIAM Journal on Control, 10 (1972), 93-98 (with G.P. McCormick).
The Metric Gradient in Normed Linear Spaces, Numerical Mathematics, 20 (1972), 115- 124 (with M. Golomb).
An Extremum Problem, SIAM Review, 14 (1972), 365.
Kantorovich Estimates for Some Convex Programs, SIAM Journal on Control, 11 (1973), 375-377 (with A.A. Goldstein).
A Characterization of Inner Product Spaces, Bulletin American Mathematical Society, 79 (1973), 530-532.
A Characterization of Inner Product Spaces, Proc. American Mathematical Society, 41 (1973), 569-574.
Optimal Error Bounds for the Newton-Kantorovich Theorem, SIAM Journal on Numerical Analysis, 11 (1974), 10-13 (with W.B. Gragg).
Newton’s Method for Problems with Equality Constraints, SIAM Journal on Numerical Analysis, 11 (1974), 174-196.
A General Approach to Newton's Method for Banach Space Problems with Equality Constraints, Bulletin American Mathematical Society, 80 (1974), 355-360.
Newton's Method for Optimization problems with Equality Constraints, SIAM Journal on Numerical Analysis, (1974), 874-886.
A Stable Approach to Newton's Method for General Mathematical Programming Problems in , SIAM Journal of Optimization Theory and Applications, 14 (1974), 453-476.
An Extension of Curry's Theorem to Steepest Descent in Normed Linear Spaces, Mathematical Programming, 9 (1975), 247-254 (with R.H. Byrd).
Nonparametric Maximum Likelihood Estimation of Probability Densities by Penalty Function Methods, Annals of Statistics, 3 (1975), 1329-1348 (with G., de Montricher and J.R. Thompson).
Computable A Posteriori L_{inf.} Error Bounds for the Approximate Solution of Two-Point Boundary Value Problems, SIAM Journal on Numerical Analysis, 12 (1975), 919-937 (with Mary Anne McCarthy).
Kernel Density Estimation Revisited, Nonlinear Analysis, Theory, Methods and Applications, 1 (1977), 339-372 (with D. Scott and J.R. Thompson).
Diagonalized Multiplier Methods and Quasi-Newton Methods for Constrained Optimization, Journal of Optimization Theory and Applications, 22 (1977), 135-194.
Quasi-Newton Methods for Constrained Optimization: Equivalence of Existing Methods and a New Implementation, in Nonlinear Programming, 3 (1978), Eds. O.L. Mangasarian, R.R. Meyer, and S.M. Robinson, Academic Press, New York, 125-164.
Optimal Smoothing of Direct Estimates of the Power Spectrum, Communications in Statistics, 4 (1978), (with R. Byrd and J. Thompson).
On the Role of Slack Variables in Quasi-Newton Methods for Constrained Optimization, in Numerical Optimization of Dynamic Systems, (1980) L.C.W. Dixon and G.P. Szegö (eds.), North Holland Press, 235-246.
Nonparametric Probability Density Estimation by Discrete Maximum Penalized Likelihood Criteria, Annals of Statistics, 8 (1980), 820-832 (with D. Scott and J.R. Thompson).
Nonlinear Programming, McGraw Hill Encyclopedia of Science and Technology, (1981).
Recent Advances in Nonlinear Programming, McGraw-Hill Yearbook of Science and Technology, (1981).
A Trust Region Strategy of Equality Constrained Optimization, in Numerical Optimization, (1984), ed. by P.T. Boggs, R.H. Byrd and R.B. Schnabel, SIAM, 71-82 (with M.R. Celis and J.E. Dennis).
A Convergence Theory for a Class of Quasi-Newton Methods for Constrained Optimization, SIAM Journal on Numerical Analysis, 24 (1987), 1133-1151 (with R. Fontecilla and T. Steihaug).
On the Characterization of q-Superlinear Convergence of Quasi-Newton Methods for Constrained Optimization, Math. Comp., 49 (1987), 581-584 (with J. Stoer).
The Projected Newton Method has Order 1 + sqrt(2) for the Symmetric Eigenvalue Problem, SIAM Journal on Numerical Analysis, 25 (1988), 1376-1382 (with David Whitley).
Secant Updates for use in General Constrained Optimization, Math. of Comp., 51 (1988), 181-202.
A Convergence Theory for the Structured BFGS Secant Method with an Application to Nonlinear Least-Squares, Journal of Optimization Theory and Applications, 61 (1989), 161-178 (with J.E. Dennis and H. Martinez).
A Cubically Convergent Method for Locating a Nearby Vertex in Linear Programming, Journal of Optimization Theory and Applications, 67 (1990), 217-225 (with Y. Zhang).
An Optimal Basis Identification Technique for Interior-Point Linear Programming Methods, Linear Algebra and Its Applications, 152 (1991), 343-363, special issue devoted to interior-point methods (with Y. Zhang).
An SQP Augmented Lagrangian BFGS Algorithm for Constrained Optimization, SIAM Journal on Optimization, 2 (1992), 210-241 (with R.H. Byrd and Y. Zhang).
On the Superlinear and Quadratic Convergence of Primal-Dual Interior-Point Linear Programming Algorithms, SIAM Journal on Optimization, 2 (1992), 304-324 (with Y. Zhang and J.E. Dennis).
Superlinear and Quadratic Convergence of Primal-Dual Interior-Point Methods for Linear Programming Revisited, Journal of Optimization Theory and Applications, 73 (1992), 229-242 (with Y. Zhang).
On the Superlinear Convergence of Interior-Point Algorithms for a General Class of Problems, SIAM Journal on Optimization, 3 (1993), 413-422 (with Y. Zhang and F. Potra).
A Superlinearly Convergent Polynomial Primal-Dual Interior-Point Algorithm for Linear Programming, SIAM Journal on Optimization, 3 (1993), 118-133 (with Y. Zhang).
Sizing the BFGS and DFP Updates: A Numerical Study, Journal of Optimization Theory and Applications, 78 (1993), 93-108 (with Martha Contreras).
A Quadratically Convergent O(sqrt(n)L)-Iteration Algorithm for Linear Programming, Mathematical Programming, 59 (1993), 151-162 (with Y. Ye, O. Guler and Y. Zhang).
On the Quadratic Convergence of the Singular Newton's Method (an essay), SIAG/OPT Views and News: A Forum for the SIAM Activity Group in Optimization, Ed. Larry Nazareth, No. 1, Fall 1992, 6-8 (with Y. Zhang).
A Unified Approach to Global Convergence of Trust-Region Methods for Optimization, (revised July 1993), Mathematical Programming, 68 (1995), 319 (with J.E. Dennis and Shou-Bai Li).
The Mehrotra Predictor-Corrector Interior-Point Method as a Perturbed Composite Newton Method, SIAM Journal on Optimization, 6 (1) (1996), 47-56 (with Y. Zhang, M.J. Saltzman, and A. Weiser).
A Study of Indicators for Identifying Zero Variables in Interior-point Methods, SIAM Review, 36 (1994), 45-72 (with A.S. El - Bakry and Y. Zhang).
On the Characterization of Q-Superlinear Convergence for Quasi-Newton Interior-Point Methods for Nonlinear Programming, El Boletin de la Sociedad Matematica Mexicana, inaugural issue of the Journal of Mexican Mathematics Society, 1(3) (1995), 137-148 (with H.J. Martinez and Z. Parada).
On the Convergence of the Iteration Sequence in Primal-Dual Interior-Point Methods, Mathematical Programming, 68 (1995), 141-154 (with Y. Zhang and Yinyu Ye).
On the Convergence of the Mizuno-Todd-Ye Algorithm to the Analytic Center of the Solution Set, to appear in SIAM Journal on Optimization, (with C. Gonzaga).
On the Quadratic Convergence of the Simplified Mizuno-Todd-Ye Algorithm for Linear Programming, SIAM Journal on Optimization, 7 (1) (1997), 66-85 (with C. Gonzaga).
An Extension of the Karush-Kuhn-Tucker Necessity Conditions to Infinite Programming, SIAM Review, 36 (1994), 1-17 (with Michael Trosset).
Numerical Experience with Polyhedral Norm CDT Trust-Region Algorithms, Journal of Optimization Theory and Applications, 85 (1995), 575-591 (with M. El-Alem).
On the Formulation and Theory of the Newton Interior-Point Method for Nonlinear Programming, Journal of Optimization Theory and Applications, 89 (1996), 507-541 (with A. El-Bakry, T. Tsuchiya and Y. Zhang).
On the Construction of Strong Complementarity Slackness Solutions for DEA Linear Programming Problems Using a Primal-Dual Interior-Point Method, to appear in The Annals of Operations Research, (with M.D. Gonzalez-Lima and R.M. Thrall).
The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method, to appear in Computational Statistics (with A. Kearsley and M. Trosset).
An Approach to Parallelizing Isotonic Regression, Applied Mathematics and Parallel Computing: Festschrift for Klaus Ritter, H. Fischer, B. Riedmuller, S. Schaffler (Editors), Physica-Verlag, Heidelberg, (1996) 141-147 (with A.J. Kearsley and M.W. Trosset).
On the Convergence Rate of Newton Interior-Point Methods in the Absence of Strict Complementarity, Computational Optimization and Applications, 6 (1996), 157-167 (with A. El-Bakry and Y. Zhang).
An Interior-Point Method with Polynomial Complexity and Superlinear Convergence for Linear Complementarity Problems, (with J. Ji, F. Potra and Y. Zhang).
Perturbation Lemma for Newton's Method with Application to the SQP Newton Method, Journal of Optimization Theory and Applications, 8(1)(1998), (with D. Cores).
On Effectively Computing the Analytic Center of the Solution Set by Primal-Dual Interior-Point Methods, SIAM Journal on Optimization, 8(1)(1998), (with M. Gonzalez-Lima and F. Potra).
A Robust Choice of the Lagrange Multiplier in the SQP Newton Method, Investigacion Operativa, 7 (1,2)(1997), (with D. Cores).
Assessing and Evaluating the Evaluation Tool - The Standardized Test, Synthesis and Proceedings of the Third Annual NISE Forum, Workshop Report No. 6, National Institute for Science Education.
Computing an Exact Solution in Interior-Point Methods for Linear Programming, Contemporary Mathematics, 252 (1999), 9-29 (withe P. Williams and A. El-Bakry).
On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior- Point Newton Method for Nonlinear Programming, Journal of Optimization Theory and Applications, 114 (1) (2001), (with M. Argaez).
Comparison of Two Sets of First-Order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds, Journal of Optimization Theory and Applications, 113 (1) (2002), (with D. Jamrog and Y. Zhang).
A Fast Newton‚s Method for Entropy Maximization in Phase Determination, SIAM Review, 57 (6) (2002), 681-685, (with Z. Wu, G. Phillips, and Y. Zhang).
The Local Behavior of Newton's Method on Two Equivalent Systems from Linear Programming, Journal of OptimizationTheory and Applications, 112 (2) (2002), 239- 263, (with C. Villalobos and Y. Zhang).
Selective Search for Global Optimization of Zero or Small Residual Least-Squares Problems: A Numerical Study, Computational Optimization and Applications, 20 (2001), 299-315, (with L. Velazquez, G. Phillips, and Y. Zhang).
On Convergence of Minimization methods: Attraction, Repulsion and Selection, Journal of Optimization Theory and Applications, 107 (2000), 529-546, (with Y. Zhang and L. Velazquez).
A Global Optimization Method for the Molecular Replacement Problem in X-ray Crystallography, Mathematical Programming B, (with D. Jamrog, G. Phillips, and Y. Zhang).
On Sizing and Shifting the BFGS Update within the Sized Broyden Family of Secant Updates, Journal on Optimization,15 (1) (2004),139–160,(with H. Yabe and H.J. Martinez).
Quantification of Regional Ventilation from Treatment Planning CT, Int. J. Radiation Oncology Biol. Phys., 62 (3) (2005), 630-634, (with T. Guerrero, K. Sanders, J. Noyola-Martinez, E. Castillo, Y. Zhang, R. Guerra, Y. Borghero, and R. Komaki).
Technical Reports
Karmarkar as a Classical Method, CAAM TR 87-7, (with M. Morshedi).
A Superlinearly Convergent O(sqrt(n)L)-Iteration Algorithm for Linear Programming, CAAM TR91-22, (with Y. Ye and Y. Zhang).
On the Convergence of Interior-point Methods to the Center of the Solution Set in Linear Programming, CAAM TR91-30, (with Y. Zhang).
The Dikin-Karmarkar Principle for Steepest Descent: Avoiding Short Steps, CAAM TR92-29, (with Catherine Samuelsen).
Logarithmic Indicators and the Identification of Subgroups of Variables in Interior-Point Methods, CAAM TR 93-35, (with A. El-Bakry and Y. Zhang).
Papers in Preperation
Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as the Projected Newton Method, (with J.E. Dennis).
An Algorithm Based on a Convenient Trust-Region Subproblem for Nonlinear Programming, (with M.R. Celis and J.E. Dennis).
Global Convergence of a Primal-Dual Interior-Point Newton Method for Nonlinear Programming Using a Modified Augmented Lagrangian Function, (with M. Argaez).
An Inexact Trust-Region Feasible-Point Algorithm for Nonlinear Systems of Equalities and Inequalities, (with M. El-Hallabi).
Computational Experience of an Augmented Lagrangian for Nonlinear Programming as a Merit Function in a Primal-Dual Interior-Point Method, (with Z. Parada).