TomSym

The TomSym MATLAB symbolic modeling engine is a platform for modeling applied optimization and optimal control problems.

Description
TomSym is complete modeling environment in Matlab with support for most built-in mathematical operators in Matlab. It is a combined modeling, compilation and interface to the TOMLAB solvers. The matrix derivative of a matrix function is a fourth rank tensor - that is, a matrix each of whose entries is a matrix. Rather than using four-dimensional matrices to represent this, TomSym continues to work in two dimensions. This makes it possible to take advantage of the very efficient handling of sparse matrices in Matlab, which is not available for higher-dimensional matrices.

TomSym has a variety of functions, among them:


 * Ability to transform expressions and generate analytical first and second order derivatives, including sparsity patterns.
 * Interfaced and compatible with MAD, i.e. MAD can be used when symbolic modeling is not suitable.
 * Numerical differentiation can be used to parts of the model.
 * Functionality for plotting and computing a variety of information for the solution to the problem.
 * Support for if, then, else statements.
 * Ability to analyze p-coded Matlab files.
 * Automated code simplification for generated models, for example.
 * Multiplication by 1 or the identity matrix is eliminated: 1*A = A
 * Addition/subtraction of 0 is eliminated: 0+A = A
 * All-same matrices are reduced to scalars: [3;3;3]+x = 3+x
 * Scalars are moved to the left in addition/subtraction: A-y = -y+A
 * Inverse operations cancel: sqrt(x)^2 = x

Modeling
The TomSym symbolic source transformation makes it possible to define any the set of decision variables (both continuous and integer) and any type of constraint as well as scalars and constant parameters.

Linear programming
An example linear programming problem would look like this:

Mixed-integer nonlinear programming
A MINLP problem is defined just like a linear programming problem. This example also shows how to convert the model into a general TOMLAB problem.

Multi-index modeling
tomSym makes it possible to build models with two or more variable indices in MATLAB. The following example creates a variable 'flow' with four indices. The variable is then used to create a constraint over two of the indices and to sum the multiplication with a two-dimensional matrix.

Automatic and numerical differentiation
For functions that cannot be interpreted by tomSym it is possible to use either automatic differentiation or numerical differentiation. In the following example a simple problem is solved using the two methods.