PSG solves the following general Optimization Problems:

 

Minimize (maximize)

                                                   [objective function]

subject to

              [general constraints]            

                                               [box constraints on decision vector]

or or             [real or boolean or integer]

 

Here:

is decision vector;

,   are linear combinations (i.e., weighted sums) of Deterministic and Risk Functions:

= real numbers,

 

= Deterministic functions,

 

= Risk Function ,

 

= number of deterministic functions included in the;

 

=  number of risk functions included in the; .

 

In PSG this formal statement of Optimization Problem is described by using the following PSG objects: Problem, Objective, Constraint, and Box (of Variables) (see Elements of Optimization Problem). Objective describes objective function in Optimization Problem; Constraint describes general constraints; Box (of Variables) describes bounds on decision vector, and their types (real, boolean, integer). Objective, Constraint, and Box (of Variables) are elements of  PSG object called Optimization Problem.

 

For solving Optimization Problem in Run-File, MATLAB, or C++ environments this mathematical formulation must be presented as Problem Statement in General (Text) Format.  In MATLAB environment Optimization Problem may be also solved by using Special PSG MATLAB Subroutines. This format creates and solves optimization problems in the standard MATLAB-format (similar to the quadprog or linrpog MATLAB subroutines).