On a supporting hyperlane for two convex polyhedral sets
Libuše Grygarová · Optimization · 1998
A calculation of all hyperplanes, which are supporting simultaneously for two convex polyhedral sets lying in the same halfspace (corresponding to such hyperplane) is dealt with in this article. In the theory of optimization this means to find every linear objective function, which attains the same maximum (or minimum) simultaneously over two feasible sets. The feasible sets are described by a finite number of linear inequalities, can be bounded or unbounded, and none of them can be a subset of the other one. Using the derived theory we try to find an approximate solution of a special nonlinear programming problem.