Name
Abstract | ||
|---|---|---|
A basic algorithm for the minimization of a differentiable convex function (in particular, a strictly convex quadratic function)
defined on the convex hull of m points in R
n
is outlined. Each iteration of the algorithm is implemented in barycentric coordinates, the number of which is equal to m. The method is based on a new procedure for finding the projection of the gradient of the objective function onto a simplicial
cone in R
m
, which is the tangent cone at the current point to the simplex defined by the usual constraints on barycentric coordinates.
It is shown that this projection can be computed in O(m log m) operations. For strictly convex quadratic functions, the basic method can be refined to a noniterative method terminating
with the optimal solution. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/s00186-005-0018-4 | Math. Meth. of OR |
Keywords | Field | DocType |
convex functions on simplexes · barycentric coordinates · projection of directions on simplexes,objective function,convex hull,convex function,tangent cone | Orthogonal convex hull,Discrete mathematics,Mathematical optimization,Convex combination,Convex set,Convex hull,Subderivative,Convex polytope,Proper convex function,Mathematics,Convex analysis | Journal |
Volume | Issue | ISSN |
62 | 2 | 1432-2994 |
Citations | PageRank | References |
2 | 0.39 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nikolai D. Botkin | 1 | 21 | 9.26 |
| J. Stoer | 2 | 155 | 51.88 |