Title: Unconstrained inverse quadratic programming problem,
Abstract: The paper covers a formulation of the inverse quadratic programming problem
in terms of unconstrained optimization where it is required to find the unknown
parameters (the matrix of the quadratic form and the vector of the quasi-linear
part of the quadratic form) provided that approximate estimates of the optimal
solution of the direct problem and those of the target function to be minimized
in the form of pairs of values lying in the corresponding neighborhoods are
only known. The formulation of the inverse problem and its solution are based
on the least squares method. In the explicit form the inverse problem solution
has been derived in the form a system of linear equations. The parameters
obtained can be used for reconstruction of the direct quadratic programming
problem and determination of the optimal solution and the extreme value of the
target function, which were not known formerly. It is possible this approach
opens new ways in over applications, for example, in neurocomputing and quadric
surfaces fitting. Simple numerical examples have been demonstrated. A scenario
in the Octave/MATLAB programming language has been proposed for practical
implementation of the method.