Unconstrained inverse quadratic programming problem
This work addresses the problem of recovering quadratic programming parameters from noisy observations, but the contribution is incremental as it applies existing least squares methods to a specific inverse formulation.
The paper formulates an inverse quadratic programming problem as unconstrained optimization, deriving an explicit solution via least squares to reconstruct unknown parameters from approximate data. Numerical examples and an Octave/MATLAB implementation are provided.
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.