@inbook{3a181bc554b0438aa373f30ba5533585,

title = "Global optimal solution to quadratic discrete programming problem with inequality constraints",

abstract = "This paper presents a canonical dual method for solving a quadratic discrete value selection problem subjected to inequality constraints. By using a linear transformation, the problem is first reformulated as a standard quadratic 0–1 integer programming problem. Then, by the canonical duality theory, this challenging problem is converted to a concave maximization over a convex feasible set in continuous space. It is proved that if this canonical dual problem has a solution in its feasible space, the corresponding global solution to the primal problem can be obtained directly by a general analytical form. Otherwise, the problem could be NP-hard. In this case, a quadratic perturbation method and an associated canonical primal-dual algorithm are proposed. Numerical examples are illustrated to demonstrate the efficiency of the proposed method and algorithm.",

keywords = "Canonical Dual Problem, Canonical Duality, Concave Maximization, Canonical Perturbation Method, Nonconvex Analysis",

author = "Ning Ruan and Gao, {David Yang}",

year = "2017",

doi = "10.1007/978-3-319-58017-3_16",

language = "English",

isbn = "9783319580166",

series = "Advances in Mechanics and Mathematics",

publisher = "Springer",

pages = "315--338",

booktitle = "Canonical Duality Theory",

edition = "1st",

}