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On the existence of...
Abstract
Ämnesord
Stäng
- We show that given a feasible primal–dual pair of linear programs in canonical form, there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, leading from the origin to the optimum. The sequence of pivots give a sequence of square and nonsingular submatrices of the constraint matrix. Solving two linear equations involving such a submatrix give primal–dual optimal solutions to the corresponding linear program in canonical form.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Linear program
- Pivoting method
- Short sequence of pivots
- Matrix algebra
- Canonical form
- Dual pairs
- Linear programs
- Nonsingular
- Optimal solutions
- Sub-matrices
- Submatrix
- Linear programming
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