Minimum norm problems over transportation polytopes
β Scribed by Achim Bachem; Bernhard Korte
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 638 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
Previous methods for solving the nonlinear one-parametric linear programming problem min (c(r)'x IAx = b, x >/ 0) for f β¬ b,PI were based on the simplex method using a considerably extended tableau. The proposed method avoids such an extension. A finite sequence of feasible bases (Bk I k = 1, 2, . .
In this paper we consider the solution of linear least squares problems min x Ax -b 2 2 where the matrix A β R mΓn is rank deficient. Put p = min{m, n}, let Ο i , i = 1, 2, . . . , p, denote the singular values of A, and let u i and v i denote the corresponding left and right singular vectors. Then
Algorithms for solving minimum norm problems are proposed using a penalty function approach and the gradient method. Numerical examples and computer simulations illustrate the results obtained.