Canonical dual approach to solving 0-1 quadratic programming problems | Zendy

ShuCherng Fang | Zendy; David Yang Gao | Zendy; Ruey-Lin Sheu | Zendy; SoonYi Wu | Zendy

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Canonical dual approach to solving 0-1 quadratic programming problems

Author(s) -

ShuCherng Fang,

David Yang Gao,

Ruey-Lin Sheu,

SoonYi Wu

Publication year - 2008

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2008.4.125

Subject(s) - dual polyhedron , duality gap , dual (grammatical number) , duality (order theory) , convexity , mathematics , canonical transformation , quadratic programming , convex analysis , strong duality , canonical form , mathematical optimization , wolfe duality , perturbation function , minification , linear programming , transformation (genetics) , convex optimization , regular polygon , weak duality , optimization problem , combinatorics , pure mathematics , art , chemistry , literature , financial economics , quantum , geometry , biochemistry , quantum mechanics , physics , economics , gene

By using the canonical dual transformation developed recently, we derive a pair of canonical dual problems for 0-1 quadratic programming problems in both minimization and maximization form. Regardless convexity, when the canonical duals are solvable, no duality gap exists between the primal and corresponding dual problems. Both global and local optimality conditions are given. An algorithm is presented for finding global minimizers, even when the primal objective function is not convex. Examples are included to illustrate this new approach.

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