부산대학교 도서관

A convex cone approach to linear programming problems is outlined. More details of this work appeared earlier in a technical report. According to the authors, this approach allows a reduction of the dimensions of the problem in certain cases; it provides opportunities for parallel computing and the possibility of quick recomputation of an optimal solution after certain changes in the parameters. The method based on cones is to find tangency conditions of an associated affine space. A method is detailed to study feasibility, boundedness and thus optimality. Relative positions of a linear subspace using concepts of strict tangency, internality and tangency are introduced. Search for extreme rays of a cone is tied to the linear independence. The authors stress the point that the theory of strict tangent relaxation is independent of any particular method used to solve a linear programming problem.