Master of Science in Applied Mathematics and Computer Science Department. Thesis (M.S.)--Eastern Mediterranean University, 1997. Includes bibliographical references (p. 34)
A variant of K. M. Anstreicher and T. Terlaky’s [Oper. Res. 42, No. 3, 556–561 (1994; Zbl 0810.90089)] monotonic build-up (MBU) simplex algorithm for linear feasibility problems is defined. Under a nondegeneracy assumption weaker than the... more
A variant of K. M. Anstreicher and T. Terlaky’s [Oper. Res. 42, No. 3, 556–561 (1994; Zbl 0810.90089)] monotonic build-up (MBU) simplex algorithm for linear feasibility problems is defined. Under a nondegeneracy assumption weaker than the usual one, the complexity of the algorithm can be given by mΔ, where Δ is a constant determined by the input data of the problem and m is the number of constraints. The constant Δ cannot be bounded in the general case by a polynomial of the bit length of the input data. Flexible index selection rules provide finiteness for strongly degenerate problems. The flexibility of the rules provides possibility to avoid numerically instable pivots. The proof of finiteness is presented in a unified framework – using the mbs-monoton property of pivot rules, defined in this paper –, that incorporates the usual minimal index rule, the Last-In-First-Out and the most-often-selected-variable index rules.
