The most-obtuse-angle row pivot rule for achieving dual feasibility: A computational study

Pan, Ping-Qi

doi:10.1016/s0377-2217(96)00027-6

Cited by 44 publications

(11 citation statements)

References 8 publications

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“…However, in our computational experiments it converges with a low iteration count on the vast majority of the tested instances. In that sense we can confirm Pan's results in [30]. On very few, mostly numerically difficult, instances it did not converge in an acceptable number of iterations.…”

Section: Pan's Methodssupporting

confidence: 81%

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Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms

Koberstein

Suhl

2007

Comput Optim Appl

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The dual simplex algorithm has become a strong contender in solving large scale LP problems. One key problem of any dual simplex algorithm is to obtain a dual feasible basis as a starting point. We give an overview of methods which have been proposed in the literature and present new stable and efficient ways to combine them within a state-of-the-art optimization system for solving real world linear and mixed integer programs. Furthermore, we address implementation aspects and the connection between dual feasibility and LP-preprocessing. Computational results are given for a large set of large scale LP problems, which show our dual simplex implementation to be superior to the best existing research and open-source codes and competitive to the leading commercial code on many of our most difficult problem instances.

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Section: Pan's Methodssupporting

confidence: 81%

“…Pan proposed this method in [29] and further examined it computationally in [30]. The basic idea is to remove at least one dual infeasibility at every iteration without giving any guarantee that no new infeasibilities are created.…”

Section: Pan's Methodsmentioning

confidence: 99%

Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms

Koberstein

Suhl

2007

Comput Optim Appl

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“…THEOREM 2. Assuming termination of Algorithm 1, it must take place at either (1) Step 1 °, with primal basic feasible solution reached; or (2) Step 6 °, detecting the infeasibility of program (1).…”

Section: Most-obtuse-angle Column Rulementioning

confidence: 99%

“…As a result, in the past a variety of pivot rules have been proposed. It is noticeable that among them the most-obtuse-angle row pivot rule is very efficient for achieving dual feasibility in the classical simplex context [1,2]. On the other hand, Pan generalized the concept of basis to include the deficient case, and established primal and dual pivot algorithms based on it [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

A basis-deficiency-allowing primal phase-I algorithm using the most-obtuse-angle column rule

Guerrero-Garcı́a

Santos-Palomo

2006

Computers & Mathematics with Applications

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The dual Phase-I algorithm using the most-obtuse-angle row pivot rule is very efficient for providing a dual feasible basis, in either the classical or the basis-deficiency-allowing context. In this paper, we establish a basis-deficiency-allowing Phase-I algorithm using the so-called most-obtuseangle column pivot rule to produce a primal (deficient or full) basis. Our computational experiments with the smallest test problems from the standard NETLIB set show that a dense projected-gradient implementation largely outperforms that of the variation of the primal simplex method from the commercial code MATLAB LINPROG vl.17, and that a sparse projected-gradient implementation of a normalized revised version of the proposed algorithm runs 34°~ faster than the sparse implementation of the primal simplex method included in the commercial code TOMLAB LPSOLVE V3.0. (~)

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“…Algorithms proposed by Pan [32][33][34][35] can be viewed as variants of the simplex algorithm. Nevertheless, some of the proposed pivot rules lead to non-monotone changes of the objective value in solution process, and produce iterates that are no longer necessarily vertices.…”

mentioning

confidence: 99%

An affine-scaling pivot algorithm for linear programming

Pan¹

2013

Optimization

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The most-obtuse-angle row pivot rule for achieving dual feasibility: A computational study

Cited by 44 publications

References 8 publications

Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms

Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms

A basis-deficiency-allowing primal phase-I algorithm using the most-obtuse-angle column rule

An affine-scaling pivot algorithm for linear programming

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