We consider the problem of finding the largest or smallest values of the objective
function F = (X,AX) + (L,X) + C in case of an **arbitrary** matrix "A" of the quadratic form.
Domain of the arguments "X" defined by a system of linear constraints-equality and linear
constraints-inequalities. Here is not imposed simplicity demand of positive definite
quadratic form in the case minimization of the function or negative definite quadratic
form in the case maximization of the function. Using quadratic functions can be
approximated an arbitrary nonlinear function (solving the problem of mathematical programming),
herewith as a rule are not expected the constant sign of the quadratic form. In this case
it is necessary to solve the optimization problem with an arbitrary matrix of the quadratic form.

It is proposed the principle of **exact** solution not based on any modification of
the gradient methods or other descent methods. The basis of finding the global extremum
of the function is taken the well-known algorithm for computing the largest or smallest
values of the function on a compact - selection of the global extremum of the set from all
local extrema inside the feasible region and on the boundary. Of course, not always a domain
defined by a system of restrictions, is compact. For an unbounded domain in the proposed
method introduces additional conditions, cutting off the compact part. Then taking the limit
as the shift of additional restrictions to infinity, we obtain an exact solution for a given
unbounded domain.

All those wishing to offer free opportunity to test above specified idea at concrete
examples. For the purity of the experiment you create the example yourself and offer to solve
it to author. After receiving solution, you can analyze it thoroughly to make sure working
capacity of the algorithm or abandon it.

**Software testing.** In order to avoid confusion in the description of
examples of problems, is designed a program. You can download it here.
This self-extracting archive file is containing four files: qpu.exe, qpu.aux, qpu.t0 and qpu.t1.
All four files must be placed in one folder, executable file - qpu.exe. The program qpu.exe allows
you to specify numerical parameters the quadratic programming problem and write them in a special
format file. This file can be sent to the author bgs@krm.net.ua,
which undertakes to solve any problem that was sent or declare of inability to obtain the
result with the claimed algorithm. In any case, response will be sent to your e-mail.

**Tasks to test online.** Numerical parameters of the quadratic programming problem
small dimension, in standard form can be entered directly:
Structure of the task -> Numerical data. In this case, the answer
will appear on this site in a few days by page
Solving quadratic programming problems
(author visits the site 1-2 times a week).

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## AutorGennadij Bulanov, 1948 yr birth, Ph.D. phys.-math. sciences, docent department of higher mathematics Donbass State Engineering Academy, Kramatorsk, Donetsk region, Ukraine. bgs@krm.net.ua |
## From the methodological developments G.Bulanov for educational purposesAutomated generator problems on functional analysis (in Russian) |