Unconstrained minimization.


Schnabel, Robert B., Koontz, John E., and Weiss, Barry E. (1985). A modular system of algorithms for unconstrained minimization. ACM Transactions on Mathematical Software, 11(4), 419-440.

Dennis, John E., Jr., and Schnabel, Robert B. (1983). Numerical methods for unconstrained optimization and nonlinear equations. Englewood Cliffs, NJ: Prentice-Hall, Inc.

Kahaner, David, Moler, Cleve, and Nash, Stephen (1989). Numerical methods and software. Englewood Cliffs, NJ: Prentice-Hall, Inc. [Sections 9.4-9.6 concern UNCMIN.]


We describe a new package, UNCMIN, for finding a local minimizer of a real valued function of more than one variable. The novel feature of UNCMIN is that it is a modular system of algorithms, containing three different step selection strategies (line search, dogleg, and optimal step) that may be combined with either analytic or finite difference gradient evaluation and with either analytic, finite difference, or BFGS Hessian approximation. We present the results of a comparison of the three step selection strategies on the problem in Moré, Garbow, and Hillstrom [1981] in two separate cases: using finite difference gradients and Hessians, and using finite difference gradients with BFGS Hessian approximations. We also describe a second package, REVMIN, that uses optimization algorithms identical to UNCMIN but obtains values of user-supplied functions by reverse communication. [Schnabel, Koontz, and Weiss, 1985, p. 419.]


Fortran 77, Fortran 90


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ORIGINAL CODE LOCATION (Fortran 77 version, individual files) (Prof. Stephen Nash’s single and double precision versions of UNCMIN in combined files) or (Fortran 90 version of software in Kanaher, Moler, and Nash, 1989, Numerical methods and software [“NMS”], including subroutines corresponding to UNCMIN.)


See the UNCMIN User’s Guide: (

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