fmincon_test

fmincon_test, a MATLAB function which calls fmincon(), which seeks the minimizer of a scalar function of multiple variables, within a region specified by linear constraints and bounds. fmincon() is part of the MATLAB Optimization Toolbox.

A related function built into MATLAB is fminsearch which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

Usage:

x_opt = fmincon ( fun, x0, A, b, Aeq, beq, lb, ub )

• fun is the "function handle"; that is, the name of an M-file that defines the function, preceded by an "@" sign;
• x0 is an initial value for the optimizer;
• A, b define a linear inequality constraint A * x <= b on the solution.
• Aeq, beq define a linear equality constraint Aeq * x = beq on the solution.
• lb, ub define bounds on the solution, lb <= x <= ub.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

fmincon_test is available in a MATLAB version.

Related Data and Programs:

asa047, a MATLAB code which minimizes a scalar function of several variables using the nelder-mead algorithm.

compass_search, a MATLAB code which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

nelder_mead, a MATLAB code which minimizes a scalar function of several variables using the nelder-mead algorithm, by jeff borggaard.

polynomials, a MATLAB code which defines multivariate polynomials over rectangular domains, for which certain information is to be determined, such as the maximum and minimum values.

praxis, a fortran90 library which implements the principal axis method of richard brent for minimization of a function without the use of derivatives.

test_opt, a MATLAB code which defines test problems requiring the minimization of a scalar function of several variables.

toms178, a MATLAB code which optimizes a scalar functional of multiple variables using the hooke-jeeves method.

Reference:

1. Harald Niederreiter, Kevin McCurley,
   Optimization of functions by quasi-random search methods,
   Computing,
   Volume 22, Number 2, 1979, pages 119-123.

Examples and Tests:

• fmincon_test.m, calls all the tests.
• fmincon_test.sh, runs all the tests.
• fmincon_test.txt, the output file.

• fmincon_test01.m, uses the Niederreiter-McCurley function #1.
• niederreiter_mccurley1.m, evaluates the Niederreiter-McCurley function #1.
• fmincon_test02.m, uses the Niederreiter-McCurley function #2.
• niederreiter_mccurley2.m, evaluates the Niederreiter-McCurley function #2.
• fmincon_test03.m, uses the Niederreiter-McCurley function #3.
• niederreiter_mccurley3.m, evaluates the Niederreiter-McCurley function #3.
• fmincon_test04.m, uses the Niederreiter-McCurley function #4.
• niederreiter_mccurley4.m, evaluates the Niederreiter-McCurley function #4.
• fmincon_test05.m, uses the Niederreiter-McCurley function #5.
• niederreiter_mccurley5.m, evaluates the Niederreiter-McCurley function #5.
• fmincon_test06.m, uses the Niederreiter-McCurley function #6.
• niederreiter_mccurley6.m, evaluates the Niederreiter-McCurley function #6.