$$

$$

$$

$$

*MPSFormat*

$$* * (the format used for reading and writing linear and quadratic
programs)

There is a class that represents the solution of a linear or quadratic program. An instance of this class is returned by any of the solution functions below.

*CGAL::Quadratic_program_solution<ET>*

We offer a number of predefined models for the above program concepts.
The following two are simultaneously models for all four concepts and
are probably the most convenient models; they allow you to construct
linear or quadratic programs entry by entry, or from streams in
*MPSFormat*. At any time, you can query these programs for
linearity and nonnegativity and thus select the appropriate
solution function.

*CGAL::Quadratic_program<NT>*

$$* * (for linear and quadratic programs that own their
data and are built entry-wise)

*CGAL::Quadratic_program_from_mps<NT>*

$$* * (for linear and quadratic programs read from an input stream in
*MPSFormat*; the constructed program can also be manipulate entry-wise)

Then there are specific models for any of the four program concepts above; these are useful if you want to maintain the program data yourself, since they simply wrap random access iterators over the program data and involve no further copying of data.

*CGAL::Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it>*

$$* * (for quadratic programs that wrap given iterators, without copying
data)

*CGAL::Linear_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, C_it>*

$$* * (for linear programs wrapping given iterators)

*CGAL::Nonnegative_quadratic_program_from_iterators<A_it, B_it, R_it, D_it, C_it>*

$$* * (for nonnegative quadratic programs, wrapping given iterators)

*CGAL::Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, C_it>*

$$* * (for nonnegative linear programs, wrapping given iterators)

In case you want to construct a program from complicated iterators (whose types you don't know, or simply don't want to bother with), we provide four makers.

*CGAL::make_quadratic_program_from_iterators*

*CGAL::make_linear_program_from_iterators*

*CGAL::make_nonnegative_quadratic_program_from_iterators*

*CGAL::make_nonnegative_linear_program_from_iterators*

There are four functions to solve a program, one for each program concept.

*CGAL::solve_quadratic_program*

*CGAL::solve_linear_program*

*CGAL::solve_nonnegative_quadratic_program*

*CGAL::solve_nonnegative_linear_program*

The solution process can customized by passing an object of the class

Programs can be written to an output stream in *MPSFormat*, using
one of the following four functions.

*CGAL::print_quadratic_program*

*CGAL::print_linear_program*

*CGAL::print_nonnegative_quadratic_program*

*CGAL::print_nonnegative_linear_program*

Next chapter: Timers, Hash Map, Union-find, Modifiers