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We study a canonical duality method to solve a mixed-integer nonconvexfourth-order polynomial minimization problem with fixed cost terms. Thisconstrained nonconvex problem can be transformed into a continuous concavemaximization dual problem without duality gap. The global optimality conditionsare proposed and the existence and uniqueness criteria are discussed.Application to a decoupled mixed-integer problem is illustrated and analyticsolution for a global minimum is obtained under some suitable conditions.Several examples are given to show the method is effective.

Canonical dual method for mixed integer fourth-order polynomial minimization problems with fixed cost terms