In many inFEASIBLE linear programs it is important to construct it to a FEASIBLE PROBLEM with a minimum parameters changing corresponding to a given nonnegative vector. This paper defines a new INVERSE PROBLEM, called “INVERSE FEASIBLE PROBLEM”. For a given inFEASIBLE polyhedron and an n-vector x0 a minimum perturbation on the parameters can be applied and then a FEASIBLE polyhedron is concluded.

In this article we consider an INVERSE PROBLEM of liner heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation term from an over specified. Condition on the boundary. We propose a numerical algorithm based on finite difference method and least square technique. Results show that an excellent estimation can be obtained for unknown functions.

This paper considers an INVERSE eigenvalue PROBLEM for bisymmetric nonnegative matrices. We first discuss the specified structure of the bisymmetric matrices. Then for a given set of real numbers of order maximum five with special conditions, we construct a nonnegative bisymmetric matrix such that the given set is its spectrum. Finally, we solve the PROBLEM for arbitrary order n in the special case of the spectrum.

In this paper, the INVERSE eigenvalue PROBLEM for the bordered diagonal matrices are reconsidered whose elements are equal to zero except for the first row, the first column and the diagonal elements. The necessary and sufficient conditions for existence of a symmetric bordered diagonal matrix from special spectral data have been determined. A new algorithm to make such matrices is derived and some numerical examples are given to illustrate the efficiency of the method.

In this paper, we consider the PROBLEM of determining of two unknown flux terms on the boundaries of parabolic type. The unknown terms are determined from two unknown over specified conditions. The uniqueness of solutions of the INVERSE PROBLEM and a system of non-linear Volterra integral equations will be shown.

In this paper, we consider an INVERSE PROBLEM for the time-fractional diffusion equation on the sphere where the final data on the sphere are given. The PROBLEM is ill-posed in the sense of Hadamard. Hence, the regularization method has to be used for the stable approximate solution. Then the well-posedness of the proposed regularizing PROBLEM and convergence property of the regularizing solution to the exact one is proved. Error estimates for this method are provided together with a selection rule for the regularization parameter.