A variation on Karmarkar's algorithm for solving linear programming problems
Mathematical Programming: Series A and B
Implementation aids for optimization algorithms that solve sequences of linear programs
ACM Transactions on Mathematical Software (TOMS)
Computer solution of linear programs
Computer solution of linear programs
A reduced-gradient variant of Karmarkar's algorithm and null-space projections
Journal of Optimization Theory and Applications
Pricing criteria in linear programming
Progress in Mathematical Programming Interior-point and related methods
Pathways to the optimal set in linear programming
on Progress in Mathematical Programming: Interior-Point and Related Methods
A "build-down" scheme for linear programming
Mathematical Programming: Series A and B
Preconditioners for indefinite systems arising in optimization
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
The effective integration of simplex and interior point techniques. part i. decomposition. part ii. null-space affine scaling
An efficient algorithm for sparse null space basis problem using ABS methods
Numerical Algorithms
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This article develops an affine-scaling method for linear programming in standard primal form. Its descent search directions are formulated in terms of the null-space of the linear programming matrix, which, in turn, is defined by a suitable basis matrix. We describe some basic properties of the method and an experimental implementation that employs a periodic basis change strategy in conjunction with inexact computation of the search direction by an iterative method, specifically, the conjugate-gradient method with diagonal preconditioning. The result of a numerical study on a number of nontrivial problems representative of problems that arise in practice are reported and discussed.A key advantage of the primal null-space affine-scaling method is its compatibility with the primal simplex method. This is considered in the concluding section, along with implications for the development of a more practical implementation.