A strictly improving linear programming alorithm based on a series of Phase 1 problems
When used on degenerate problems, the simplex method often takes a number of degenerate steps at a particular vertex before moving to the next. In theory (although rarely in practice), the simplex method can actually cycle at such a degenerate point. Instead of trying to modify the simplex method to avoid degenerate steps, we have developed a new linear programming algorithm that is completely impervious to degeneracy. This new method solves the Phase II problem of finding an optimal solution by solving a series of Phase I feasibility problems. Strict improvement is attained at each iteration in the Phase I algorithm, and the Phase II sequence of feasibility problems has linear convergence in the number of Phase I problems. When tested on the 30 smallest NETLIB linear programming test problems, the computational results for the new Phase II algorithm were over 15% faster than the simplex method; on some problems, it was almost two times faster, and on one problem it was four times faster.
- Research Organization:
- Stanford Univ., CA (United States). Systems Optimization Lab.
- Sponsoring Organization:
- USDOE; USDOD; National Science Foundation (NSF); USDOE, Washington, DC (United States); Department of Defense, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- FG03-92ER25116
- OSTI ID:
- 5159733
- Report Number(s):
- SOL-92-2; ON: DE92015905; CNN: ECS-8906260; DMS-8913089; N00014-89-J-1659
- Country of Publication:
- United States
- Language:
- English
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