Cubically convergent method for locating a nearby vertex in linear programming | Zendy

R. A. Tapia | Zendy; Y. Zhang | Zendy

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Cubically convergent method for locating a nearby vertex in linear programming

Author(s) -

R. A. Tapia,

Y. Zhang

Publication year - 1990

Publication title -

journal of optimization theory and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.109

H-Index - 91

eISSN - 1573-2878

pISSN - 0022-3239

DOI - 10.1007/bf00940473

Subject(s) - mathematics , linear programming , sequence (biology) , vertex (graph theory) , sign (mathematics) , rate of convergence , zero (linguistics) , theory of computation , convergence (economics) , combinatorics , mathematical optimization , mathematical analysis , algorithm , computer science , graph , genetics , linguistics , philosophy , economics , biology , economic growth , channel (broadcasting) , computer network

Given a point sufficiently close to a nondegenerate basic feasible solutionx* of a linear program, we show how to generate a sequence {pk} that converges to the 0–1 vector sign(x*) at aQ-cubic rate. This extremely fast convergence enables us to determine, with a high degree of certainty, which variables will be zero and which will be nonzero at optimality and then constructx* from this information.

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