TOMS178
Minimization by Hooke-Jeeves Direct Search

TOMS178 is a FORTRAN90 library which uses the Hooke-Jeeves direct search algorithm to seek the minimizing point of a function F(X) of several variables.

The Hooke_Jeeves algorithm does not required the function F(X) to be differentiable. It does not even require the function to be continuous, although it should probably only be "weakly discontinuous", like a step function, with finitely many well-separated jumps. In any case, the algorithm only examines function values, never derivatives, remembers the location of the best value encountered, and seeks to improve this value by a clever pattern search.

The user supplies a quantity rho, between 0 and 1, which controls how cautious or daring the search is, as well as a routine to evaluate the function, and a few input parameters.

The first publication of code for the algorithm was an Algol formulation by Arthur Kaupe.

A C version of the algorithm, as written by Mark Johnson, is available at http://www.netlib.org/opt/hooke.c

Related Data and Programs:

ASA047 is a FORTRAN90 library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

DQED a FORTRAN90 library which solves constrained least squares problems.

COORDINATE_SEARCH is an executable MATLAB program which minimizes a scalar function of several variables using the coordinate search algorithm.

ENTRUST is an executable MATLAB program which minimizes a scalar function of several variables using trust region methods.

fminsearch is a MATLAB built in command which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

MINPACK a FORTRAN90 library which solves systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.

NELDER_MEAD an executable MATLAB program which minimizes a scalar function of multiple variables using the Nelder-Mead algorithm.

NL2SOL a FORTRAN90 library which implements an adaptive nonlinear least-squares algorithm.

PRAXIS a FORTRAN90 library which minimizes a scalar function of several variables, without derivative information.

TEST_NLS a FORTRAN90 library which defines test problems requiring the least squares minimization of a set of nonlinear functions.

TEST_OPT a FORTRAN90 library which defines test problems requiring the minimization of a scalar function of several variables.

TOMS178 is also available in a C version and a C++ version and a FORTRAN77 version and a MATLAB version.

TOMS611 a FORTRAN90 library which optimizes a scalar functional of multiple variables.

UNCMIN is a FORTRAN77 library which can be used to seek the minimizer of a scalar functional of multiple variables.

• M Bell, Malcolm Pike,
  Remark on Algorithm 178: Direct Search,
  Communications of the ACM,
  Volume 9, Number 9, September 1966, page 684.
• Robert Hooke, Terry Jeeves,
  Direct Search Solution of Numerical and Statistical Problems,
  Journal of the ACM,
  Volume 8, Number 2, April 1961, pages 212-229.
• Arthur Kaupe,
  Algorithm 178: Direct Search,
  Communications of the ACM,
  Volume 6, Number 6, June 1963, page 313.
• FK Tomlin, LB Smith,
  Remark on Algorithm 178: Direct Search,
  Communications of the ACM,
  Volume 12, Number 11, November 1969, page 637-638.

Source Code:

• toms178.f90, the source code;
• toms178.csh, commands to compile the source code;

Examples and Tests:

• toms178_prb.f90, the sample calling program;
• toms178_prb.csh, commands to compile, link and run the sample calling program.
• toms178_prb_output.txt, the output file.

List of Routines:

• BEST_NEARBY looks for a better nearby point, one coordinate at a time.
• HOOKE seeks a minimizer of a scalar function of several variables.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.