A new polynomial-time algorithm for linear programming
Combinatorica
A variation on Karmarkar's algorithm for solving linear programming problems
Mathematical Programming: Series A and B
A simultaneous iterative method for computing projections on polyhedra
SIAM Journal on Control and Optimization
A computational solution of the inverse problem in radiation-therapy treatment planning
Applied Mathematics and Computation
Affine-scaling for linear programs with free variables
Mathematical Programming: Series A and B
Limiting behavior of the affine scaling continuous trajectories for linear programming problems
Mathematical Programming: Series A and B
Global convergence of the affine scaling methods for degenerate linear programming problems
Mathematical Programming: Series A and B - Special issue on interior point methods for linear programming: theory and practice
Mathematics of Operations Research
On the convergence of the affine scaling algorithm
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Superlinear convergence of the affine scaling algorithm
Mathematical Programming: Series A and B
Theorems of the alternative and duality
Journal of Optimization Theory and Applications
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
The Affine Scaling Algorithm Fails for Stepsize 0.999
SIAM Journal on Optimization
Extensions of Hildreth’s Row-Action Method for Quadratic Programming
SIAM Journal on Control and Optimization
Computational experience with a dual affine variant of Karmarkar's method for linear programming
Operations Research Letters
Editorial: Nonparametric and Robust Methods
Computational Statistics & Data Analysis
Editorial: 2nd Special issue on matrix computations and statistics
Computational Statistics & Data Analysis
Robust polynomial classifier using L1-norm minimization
Applied Intelligence
| Hi-index | 0.03 |
The need for solving a system of linear inequalities arises in many applications. In some cases it is not known in advance whether the system is solvable or not. If the system happens to be inconsistent then it is often desirable to calculate a point for which the violating part of the residual vector has a minimal norm. The use of the ''robust''@?"1 norm is of particular interest. A new theorem of the alternative is established to characterize the optimality conditions and the duality relations of the resulting least absolute deviations problem. The structure of the dual problem paves the way for effective implementation of the affine scaling algorithm. Numerical experiments illustrate interesting features of the proposed method.