Abstract
This paper considers a new canonical duality theory for solving mixed integer quadratic programming problem. It shows that this well-known NP-hard problem can be converted into concave maximization dual problems without duality gap. And the dual problems can be solved, under certain conditions, by polynomial algorithms.
Highlights
Mixed integer nonlinear programming refers to optimization problems which involve continuous and discrete variables [8]
This paper considers a new canonical duality theory for solving mixed integer quadratic programming problem
It shows that this well-known NP-hard problem can be converted into concave maximization dual problems without duality gap
Summary
Mixed integer nonlinear programming refers to optimization problems which involve continuous and discrete variables [8]. We consider the following constrained mixed integer quadratic programming:. The difficulty for developing an efficient method for such mixed integer programming lies on the nonlinearity of the functions involved, and on existence of both discrete and continuous variables [20]. If we introduce the canonical duality with some strategy, we can find global optima in polynomial time [10, 11, 12].
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