MATLAB Optimization Toolbox

Linear programming, quadratic programming, unconstrained and constrained optimization of nonlinear functions, nonlinear equations, nonlinear least squares, minimax, multiobjective optimization, semi-infinite programming.

Linear programming --- a variant of the simplex method. An initial phase is needed to identify a feasible point

Quadratic programming --- an active set method. A linear programming problem is solved to determine an initial feasible point.

Unconstrained minimization --- two routines are supplied. One implements a quasi-Newton algorithm, using either DFP or BFGS to update an approximate inverse Hessian, according to a switch selected by the user. Gradients may be supplied by the user; if they are not, finite differencing is used. The second routine uses the Nelder-Mead simplex algorithm, for which derivatives are not needed.

Constrained minimization --- sequential quadratic programming. The BFGS formula is used to maintain an approximation to the Hessian. Han's merit function is used to determine the step length at each iteration.

Nonlinear equations --- Newton's method and the Levenberg-Marquardt algorithm are supplied. The user chooses the algorithm by setting a switch.

Nonlinear least squares --- the Gauss-Newton method and the Levenberg-Marquardt method are supplied. The user makes the choice.

Minimax --- these problems can be formulated as constrained optimization problems, and a sequential quadratic programming algorithm is used to solve them here. Advantage is taken of the structure of the problem in the choice of approximate Hessian.

Multiobjective optimization --- The problem is formulated as one of decreasing a number of objective functions below a certain threshold simultaneously, so it is viewed as a constrained optimization problem. Again, sequential quadratic programming is used to solve it.

Semi-infinite programming --- Cubic and quadratic interpolation is used to locate peaks in the infinite constraint set and therefore to reduce the problem to a constrained optimization problem.

The software is made available as MATLAB M-files. It executes on any environment that supports MATLAB (including most PC and workstation environments in common use, as well as the Alliant family and the Cray UNICOS environment). The user supplies the function and constraint information to the toolbox as an M-file or as a series of MATLAB statements. If the functions are too complicated to be expressed as MATLAB statements, the MATLAB facilities for interfacing to Fortran and C routines can be invoked.

Need more info?

Visit the Optimization Toolbox homepage.

Or contact:

The MathWorks, Inc.
24 Prime Park Way
Natick MA   01760
Phone: (508) 647-7000
Fax: (508) 647-7101
Email: info@mathworks.com

Reference:

A. Grace, Optimization Toolbox User's Guide, The MathWorks, Inc., 1990.

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