Optimization Problem

Optimization Problem is an object connecting vector of decision variables (PSG Point), data in the form of PSG Matrix and Functions to find optimal solution (i.e., to find the best decision vector in a feasible set). Feasible decision vectors have to satisfy some restrictions (Constraints). The quality of a feasible decision vector is measured by some criteria called an objective function (Objective) . An optimization problem is a minimization or a maximization problem. The minimization (maximization) problem minimizes (maximizes) an objective function. An optimal decision vector is a feasible vector for which the objective function attains maximum (or minimum depending upon the type of the optimization problem).

Optimization Problem can be solved in four programming environments: Shell, Run-File, MATLAB, and C++.

In PSG, Optimization Problem consists of Elements of Problem: Objective, Constraint,  and Box (of Variables).

As a tool for searching optimal solution of Optimization Problem, PSG provides Solvers. For calculating Objective, Constraints, and Functions at optimal Point, PSG provides object Value.

The section "Mathematical Optimization Problem Statement" presents general mathematical formulation of Optimization Problem.

For solving Optimization Problem in Run-File, C++ or MATLAB environments this mathematical formulation must be presented in General (Text) Format of PSG. 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).