Solutions and optimality criteria to box constrained nonconvex minimization problems
By David Yang Gao. 2007
83 citations recorded by the source corpus.
This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. It is proved that under certain conditions, the constrained nonconvex problems can be converted to the so-called canonical (perfect) dual problems, which can be solved by deterministic methods. Both global and local extrema of the primal problems can be identified by a triality theory proposed by the author. Applications to nonconvex integer programming and Boolean least squares problems are discussed. Examples are illustrated. A conjecture on NP-hard problems is proposed.
Subfields: Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/f3e259059c999ef5929aada8f8bdd7685b1c3e3e
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In Computational Theory and Mathematics
In Numerical Analysis
Citations in the corpus
- Canonical dual approach to solving 0-1 quadratic programming problems (2008, background): “When the integer constraints in Xa is relaxed, the problem (P) becomes the following quadratic minimization problem with box constraints as studied in [7]: (Pbox) : min / max { P (x) = 1 2 x Qx− x f | 0 ≤ x ≤ 1 } .”
- A review of recent advances in global optimization (2009, methodology): “Based on the same method, Gao (2005) also presented a duality theory for solving concave minimization problems subject to nonlinear inequality constraints, and polynomial programming problems subject to box constraints (Gao 2007).”