On stable least squares solution to the system of linear inequalities

2007 ◽  
Vol 5 (2) ◽  
pp. 373-385 ◽  
Author(s):  
Evald Übi
Keyword(s):  
Least Squares ◽  
Linear Inequalities ◽  
System Of Linear Inequalities ◽  
Least Squares Solution

scholarly journals Modified Han algorithm for inconsistent linear inequalities

2015 ◽  
Vol 31 (1) ◽  
pp. 45-52
Author(s):  
DOINA CARP ◽  
◽  
CONSTANTIN POPA ◽  
CRISTINA SERBAN ◽  
◽  
...  
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Numerical Experiments ◽  
Linear Inequalities ◽  
Convergence Properties ◽  
Minimal Norm ◽  
Direct Solver ◽  
Least Squares Solution ◽  
Inconsistent Systems ◽  
Systems Of Linear Inequalities

In this paper we present a modified version of S. P. Han iterative method for solving inconsistent systems of linear inequalities. Our method uses an iterative Kaczmarz-type solver to approximate the minimal norm least squares solution of the problems involved in each iteration of Han’s algorithm. We prove some convergence properties for the sequence of approximations generated in this way and present numerical experiments and comparisons with Han’s and other direct solver based methods for inconsistent linear inequalities.

Mathematical programming via the least-squares method

2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Evald Übi
Keyword(s):  
Least Squares ◽  
Dual Problem ◽  
Least Squares Method ◽  
Linear Inequalities ◽  
Initial Solution ◽  
Test Problems ◽  
Minimal Norm ◽  
Stable Algorithm ◽  
System Of Linear Inequalities ◽  
Linear And Nonlinear Programming

AbstractThe least-squares method is used to obtain a stable algorithm for a system of linear inequalities as well as linear and nonlinear programming. For these problems the solution with minimal norm for a system of linear inequalities is found by solving the non-negative least-squares (NNLS) problem. Approximate and exact solutions of these problems are discussed. Attention is mainly paid to finding the initial solution to an LP problem. For this purpose an NNLS problem is formulated, enabling finding the initial solution to the primal or dual problem, which may turn out to be optimal. The presented methods are primarily suitable for ill-conditioned and degenerate problems, as well as for LP problems for which the initial solution is not known. The algorithms are illustrated using some test problems.

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