David F. Shanno

Professor Emeritus

RUTCOR, The Rutgers Center for Operations Research

Rutgers School of Business, Newark and New Brunswick






            Ph.D. - Carnegie-Mellon Univ., 1967; Major: Mathematics.

            M.S.  -  Carnegie-Mellon Univ., 1962; Major: Mathematics.

            B.A.  -  Yale University, 1959; Major: Math-Philosophy.




            E.M.L. Beale - W.B. Orchard-Hayes Prize for Excellence in Computational Mathematical Programming, Mathematical Programming Society, 1991, (with I.J. Lustig and R.E. Marsten).



            Computer Science Technical Section Prize for Research Excellence in the Interface Between Operations Research and Computer Science - Operations Research Society of America, 1992, (with I.J. Lustig and R.E. Marsten, joint with M. Kojima, N. Megiddo, T. Noma and A. Yoshise).


            INFORMS Fellow - 2005


Professional Societies


            INFORMS, SIAM, and the Mathematical Programming Society.


Professional Activities


            Associate Editor, Journal of Optimization Theory and Applications, 1982 - 1990.


            Associate Editor, Mathematical Programming, 1980 - 1989.


            Departmental Editor, MS/OR, Communications of the ACM, 1973 - 1980.




            "An accelerated gradient projection method for linearly constrained nonlinear estimation," SIAM J. APPLIEDMATH.,18, (2), March 1970, pp. 322-334.


"Conditioning of quasi-Newton methods for function minimization, "MATH. COMP., 24, (3), July 1970, pp. 647-656.


            "Optimal conditioning of quasi-Newton methods," MATH. COMP., 24, (3) July 1970, pp. 657-665 (with P.C. Kettler).


            "Parameter selection for modified Newton methods for function minimization," SIAM J. NUM. ANAL., 7, (3), September 1970, pp. 366-372.


            "Linear programming with absolute value functionals," OPER. RES., 19, (1), January-February 1971, pp. 120-124 (with R.L. Weil).


"An improved Marguardt procedure for nonlinear regressions," TECHNOMETRICS, 13,(1),

February 1971,  pp. 63-74 (with F.B. Smith).


            "Management science: A view from nonlinear programming," COMM. ACM, 15, (7), July 1972, pp. 542-549 (with R.L. Weil).


"The simplex method in mixed integer and integer programming - A unified computational view," INFOR, 11 (2), June 1973, pp. 150-162.


"Restarts and rotations of quasi-Newton methods," INFORMATION PROCESSING, 74, J.L. Rosenfeld, ed., North Holland, 1974, pp. 557-561 (with A. Berg and G. Cheston).


"The design of a prototype management decision system," INFOR., 12, (3), October 1974, pp. 341-344 (with R.N. Wolff).


"Effective comparison of unconstrained optimization techniques," MANAGEMENT SCIENCE, 22, (3), November 1975, pp. 321-330 (with K.H. Phua).


"Minimization of unconstrained multivariate functions," TRANS. ON MATH. SOFTWARE, 2, (3), March 1976, pp. 87-94 (with K.H. Phua).


            "The separate phases method of accounting for leveraged leases: Properties of the allocating rate and an algorithm for finding it," J. ACCOUNTING RESEARCH, 14, (2), Autumn 1976, pp. 346-356 (with R.L. Weil.)


"Inexact step lengths and quasi-Newton methods," INFORMATION PROCESSING, 77, B. Gilchrist, ed., North Holland, 1977, pp. 189-193 (with K.H.Phua).


"Matrix conditioning and nonlinear optimization," MATH PROG., 14, (2), March 1978, pp. 149-160 (with K.H. Phua).


"Conjugate gradient methods with inexact searches,"  MATH.  OF  OPER.  RES., 3, (3), August 1978, PP. 507-518.


            "Numerical comparison of several variable metric algorithms," JOTA, 25, (4), August 1978, pp. 507-518 (with K.H. Phua).


"On the convergence of a new conjugate gradient algorithm," SIAM J. NUM. ANAL., 15, (6), December 1978, pp. 1247-1257.


"Quadratic termination of conjugate gradient algorithms," EXTREMAL METHODS AND SYSTEMS ANALYSIS, A.V. Fiacco and K.O. Kortanek, eds., Springer-Verlag, 1980, pp. 433-441.


"On variable metric methods for sparse Hessians," MATH. COMP., 34, (150), April 1980, pp. 499-514.


"Remark on algorithm 500.  Minimization of unconstrained multivariate functions," TRANS. ON MATH. SOFTWARE, 6, (4), December 1980, pp. 618-622 (with K.H. Phua).


"On preconditioned conjugate gradient methods," NONLINEAR PROGRAMMING IV, Mangasarian, Meyer, and Robinson, eds., Academic Press, New York, 1981 pp. 201-222.


"Computational experience with methods for estimating sparse Hessians for nonlinear optimization," JOTA, 35, (2), October 1981, pp. 183-193.


            "Conjugate gradient methods for linearly constrained nonlinear programming," MATH.PROG.STUDY, 16, April 1982.pp. 149-161 (with R.E. Marsten).


"Computational testing of a large scale linearly constrained nonlinear optimization code," NONLINEAR OPTIMIZATION, 1981, M.J.D. Powell, ed., Academic Press, New York, 1982, pp. 155-160.


"Recent advances in gradient based unconstrained optimization techniques for large problems," TRANSACTIONS OF THE ASME, 105, (2), June 1983, pp. 155-159.


"Large scale unconstrained optimization," COMPUTERS AND CHEMICAL ENGINEERING, 7, (5), 1983, pp. 569-574.


            "A note on solving nonlinear minimax problems via a differentiable penalty function," JOTA, 46, (1), May 1985, pp. 95-104 (with Lyn Whitaker).


"An example of numerical nonconvergence of a variable metric method," JOTA, 46, (1), May 1985, pp. 87-94.


            "Globally convergent conjugate gradient algorithms," MATH. PROG., 33, (1) September 1985, pp. 61-67.


"Numerical methods for robust regression: Linear models," SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 7, (1), January 1986, pp. 86-97 (with D.M. Rocke).


"The scale problem in robust regression M-estimates," JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 24. (1)           1986, PP. 47-69 (with D.M. Rocke).


            "Option pricing when the variance is changing," JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS, 22, (21), June 1987, pp. 143-151 (with H. Johnson).


            "Adding variables to quasi-Newton Hessian approximations," JOTA, 54, (3), September 1987, pp. 575-582 (with K.H. Phua).


            "Gradient based unconstrained optimization methods", OPTIMIZATION, TECHNIQUES AND APPLICATIONS, K.L. Teo, H. Paul, K.L. Chen and C.M. Wang, eds.,  The National University of Singapore, 1987, pp. 95-106.


            "A reduced gradient variant of Karmarkar's algorithm and null space projections," JOTA, 57, (3) June 1988, pp. 383-397 (with R.E. Marsten).


"Computing Karmarkar projections quickly," MATHEMATICAL PROGRAMMING, 41, (1), May 1988, pp. 61-72.


"Numerical experience with sequential quadratic programming algorithms for equality constrained nonlinear programming," TOMS 15, (1), March 1989, pp. 49-63 (with K.H. Phua).


"An implementation of a primal-dual interior point method for linear programming," ORSA JOURNAL ON COMPUTING, 1, (2), Spring 1989, pp. 70-83, (with K.A. McShane and C.L. Monma).


"A unified view of interior point methods for linear programming," ANNALS OF OPERATIONS RESEARCH 22,1990,55-70, July 1988 (with A. Bagchi).


"Implementation of a dual affine interior point algorithm for linear programming," ORSA JOURNAL ON COMPUTING 1, (4). Fall 1989, 287-297 (with R.E. Marsten, M.J.Saltzman, J.F. Ballintijn and G.S. Pierce).


"Interior point methods for linear programming: just call Newton, Lagrange, and Fiacco and McCormick", INTERFACES 40, 1990, 105-116 (with R.E. Marsten, R. Subramanian, M. Saltzman and I. Lustig).


"Recent advances in numerical techniques for large scale optimization," NEURAL NETWORKS FOR CONTROL, W.T. Miller, R. Sutton, and P. Werbos, ess. MIT Press 1990, 171-178.


"Further development of a primal-dual interior point method," ORSA JOURNAL ON COMPUTING 2,1990,304-311 (with I.C. Choi and C.L. Monma).


"Computational experience with a primal-dual interior point method for linear programming," JOURNAL OF LINEAR ALGEBRA & APPLICATIONS 152, 1991, 191-222 (with I.J. Lustig and R.E. Marsten).


"The primal-dual interior point method on the CRAY supercomputer," LARGE SCALE NUMERICAL OPTIMIZATION, T. Coleman, ed., SIAM, 1990, 70-80 (with I.J. Lustig and R.E. Marsten).


            "On implementing Mehrotra's predictor - corrector interior point method for linear programming", SIAM JOURNAL ON OPTIMIZATION 2, 1992, 435-449 (with I.J. Lustig and R.E. Marsten).


            "The interaction of algorithms and architectures for interior point methods", ADVANCES IN OPTIMIZATION AND PARALLEL COMPUTING, P. Pardolos, ed., Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 1992, 190-205 (with I.J. Lustig and R.E. Marsten).


            "The interior point method for linear programming", IEEE SOFTWARE 9, July 1992, 61-68 (with G. Asfalk, I.J. Lustig, and R.E. Marsten).


            "Separable quadratic programming via a primal-dual interior point method and its use in a sequential procedure," ORSA JOURNAL ON COMPUTING 5, 1993, 182-191 (with T.J. Carpenter, I.J. Lustig, and J.M. Mulvey).


            "Very large-scale linear programming: A case study in combining interior point and simplex methods," OPERATIONS RESEARCH 40, 1992, 885-897 (with R.E. Bixby, J.W. Gregory, I.J. Lustig and R.E. Marsten).


"Higher order predictor-corrector interior point methods with application to quadratic objectives," SIAM JOURNAL ON OPTIMIZATION 3, 1993, 696-725 (with T.J. Carpenter, I.J. Lustig and J.M. Mulvey).


            "An interior point method for quadratic programs based on conjugate projected gradients," COMPUTATIONAL OPTIMIZATION & APPLICATIONS, 2, 1993, 5-28 (with T.J. Carpenter).


            "Interior point methods for linear programming; computational state of the art," ORSA JOURNAL ON COMPUTING 6, 1994, 1-14 (with I.J. Lustig and R.E. Marsten).


            "Preliminary computational experience with modified log-barrier functions for large-scale nonlinear programming," LARGE SCALE OPTIMIZATION: STATE OF THE ART, W.W. Hager, D.W. Hearn and P.M. Pardolos, Editors, Kluwer Academic Publishers, 1994, 45-67, (with M.G. Breitfeld).


            "Computational experience with a globally convergent primal-dual predictor-corrector algorithm for linear programming," MATH PROGRAMMING, 66, 1994, 123-135 (with I.J. Lustig and R.E. Marsten).


            "Computational experience with logarithmic barrier methods for linear and nonlinear comlementarity problems," OPERATIONS RESEARCH: METHODS, MODELS AND APPLICATIONS, J.E. Aronson & S. Zionts, eds., Quorum Books Westport, Connecticut, 1998, 113-130.


            "Computational experience with modified log-barrier methods for nonlinear programming," ANNALS OF OPERATIONS RESEARCH 62, 1996, 439-464, (with M.G. Breitfeld).


            "Computational methods for linear programming," ALGORITHMS FOR CONTINUOUS OPTIMIZATION, E. Spedicato, ed. Kluwer Academic Publishers, 1994, 383-414.


            "A globally convergent penalty-barrier algorithm for nonlinear programming," OPERATIONS RESEARCH PROCEEDINGS 1994, V. Derigs, A. Bachem, and A. Drexl, Editors, Springer-Verlag, 1995, 22-27 (with M.G. Breitfeld).


            "An infeasible-interior-point method for linear complementarily problems," SIAM JOURNAL ON OPTIMIZATION 7, 1997, 620-640 (with E.M. Simantiraki).


            "Implementing barrier methods for nonlinear programming," INTERIOR POINT METHODS FOR OPTIMIZATION, T. Terlaky, ed. Kluwer, 1996, 399-414 (with M.G. Breitfeld and E.M. Simantiraki).


            "Interior point methods for linear and nonlinear programming," THE STATE OF THE ART IN NUMERICAL ANAYLSIS, I.A. Duff and G.A. Watsons, eds. Oxford, New York, 1997, 339-362 (with E.M. Simantiraki).


            "An infeasible-interior-point algorithm for solving mixed complementary problems," COMPLEMENTARITY AND VARIATIONAL PROBLEMS, STATE OF THE ART, M.C. Ferris and J.S. Pang, eds., SIAM, Philadelphia, 1997, 386-404 (with E.M. Simantiraki).


            "An interior point algorithm for nonconvex nonlinear programming," COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 13, 1999, 231-252, (with R.J. Vanderbei).


            "Interior point methods for nonconvex nonlinear programming: Orderings and higher order methods", MATHEMATICAL PROGRAMMING, 87, 2000, 303-316, (with R. J. Vanderbei).


"Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions", COMPUTATIONAL OPTIMIZATION AND APPLICATIONS  23, 2, 2002, 257-272,(with H.Y. Benson and R.J. Vanderbei).


"A comparative study of large-scale nonlinear optimization algorithms", HIGH PERFORMANCE ALGORITHMS AND SOFTWARE FOR NONLINEAR OPTIMIZATION, Gianni Di Pillo and Almerico Murli, eds. Kluwer Academic Publishers, Norwell, MA 2003, 95-128, (with H.Y. Benson and R.J. Vanderbei).


            "Interior-point methods for nonconvex nonlinear programming: Jamming and numerical testing" MATHEMATICAL PROGRAMMING, Ser. A 99, 2004, 35-48 (with H.Y. Benson and R.J. Vanderbei).


            "Interior-point algorithms, penalty methods and equilibrium problems", COMPUTATIONAL OPTIMIZATION AND APPLICATIONS  34,2, June 2006, 155-182 (with H.Y. Benson, A. Sen, and R.J. Vanderbei).


           "An exact primal-dual penalty method approach to warmstarting interior-point methods for linear programming", COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 38(3), December 2007, 371-399,(with H. Y. Benson)


            "Interior-point methods for nonconvex nonlinear programming: regularization and warmstarting",  COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 40(2), June 2008, 143-189, (with H.Y. Benson).


             "Convergence analysis of a primal-dual interior-point method for nonlinear programming", ALGORITHMIC OPERATIONS RESEARCH, 3(1), 2008,(with I. Griva and R.J. Vanderbei and H. Y. Benson).


            "Optimization and dynamical systems algorithms for finding equilibria of stochastic games", OPTIMIZATION METHODS AND SOFTWARE, 23(6), December 2008, 975-993, (with A. Sen).


Working Papers


             " Interior-point method for nonconvex nonlinear programming: convergence analysis and computational experience", (with H. Benson and A. Sen)