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Linear programming is the study of optimizing a linear function over a set of linear inequalities. The Simplex Method, Ellipsoid Method and Interior Point Method are popular algorithms to solve linear programs.

3 votes
1 answer
532 views

Solving a system of linear inequalities

Consider the following system of inequalities: $Ax=b$; $x\geq 0$; A is a $m\times n$ (non-square) and sparse matrix in which some part of entries are rational. How this system can be solved without …
2 votes
0 answers
230 views

Consistency of a system of linear equations

I have a system of linear equations in form of $AX=b$ where $A_{m\times n}$, $X_{n\times 1}$ and $b_{m\times 1}$. Coefficient matrix $A$ is quite sparse. However, using a practical LP solver like LING …