The convex combinations problem
by
I G Sheremet
GiproNII

The convex combinations problem

I.G.Sheremet

34, Bld.12-A, A.Nevskogo Str., Novosibirsk, 630065, Russia, USSR E-mail: agk@neic.nsk.su

Let {v_i, i=1, ..., m}, v are given vectors. Consider the following convex combinations problem (CCP): indicate all coefficients x_i, i=1, ..., m of convex combinations of the vectors {v_i, i=1, ..., m} giving the point v . Solve CCP for all simplex of the polyhedron conv{v_i, i=1, ..., m} containing v and denote the finite set of such solutions by {P_n, n=1, ..., N}.

Theorem Solutions of the CCP are conv{P_n, n=1, ..., N}.

The effective numerical algorithm constructing {P_n, n=1, ..., N} is developed.

Date received: October 31, 2000