In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

The purpose of this paper is describes the use of grey pridiction in linear programming problems. Some definitions and concepts of grey system theory are introduced and then, we introduced GM(1,1) and fractional order accumulation into grey model. Due to the fluctuation of prices and the lack of certainty data in the market, optimal production was calculated to optimize the profit from sales us...

In this paper we prowide lower bounds on the complexity of the DNF exception problem for short exception lists and hypercube covering problem. The method proposed is based on the relaxation of the initial problem to a certain linear programming problem. Some explicit bounds are provided for the case when exception list size is bounded above by a logarithm of dimension. The bound provided in thi...

Hierarchical multimodal hub location problem is a cost-minimizing hub covering problem where two types of hubs and hub links, accounting for ground and air transportation, are to be established, while ensuring time-definite deliveries. We propose a mixed-integer programming formulation and perform a comprehensive sensitivity analysis on the Turkish network. We show that the locations of airport...

We de ne a natural product on integer programming problems with nonnegative coe cients. Hypergraph covering problems are a special case of such integer programs, and the product we de ne is a generalization of the usual hypergraph product. The main theorem of this paper gives a su cient condition under which the solution to the nth power of an integer program is asymptotically as good as the so...