Description:
In this article, we first introduce a definition of a local minimizer for the quadratic programs with {-1, 1} constraints and show that the existing necessary condition of global optimality in some recent literature is in fact the necessary and sufficient condition of local optimality under the present definition. A filled function and the corresponding filled function algorithm then are proposed to get the global minimizer of the concerned minimization problem. The existing sufficient condition of global optimality is employed to form one of the termination rules of the algorithm. Several numerical examples are reported to show the efficiency of the present method for solving quadratic programs with binary constraints.
Description:
In this paper we establish conditions which ensure that a feasible point is a global minimizer of a quadratic minimization problem subject to box constraints or binary constraints. In particular, we show that our conditions provide a complete characterization of global optimality for non-convex weighted least squares minimization problems. We present a new approach which makes use of a global subdifferential. It is formed by a set of functions which are not necessarily linear functions, and it enjoys explicit descriptions for quadratic functions. We also provide numerical examples to illustrate our optimality conditions.
Description:
In this paper, some verifiable necessary global optimality conditions and sufficient global optimality conditions for some classes of polynomial integer programming problems are established. The relationships between these necessary global optimality conditions and these sufficient global optimality conditions are also discussed. The main theoretical tool for establishing these optimality conditions is abstract convexity.
Description:
In this paper, some verifiable necessary global optimality conditions and sufficient global optimality conditions for some classes of polynomial integer programming problems are established. The relationships between these necessary global optimality conditions and these sufficient global optimality conditions are also discussed. The main theoretical tool for establishing these optimality conditions is abstract convexity.
Description:
In this paper, we consider a class of mixed integer weakly concave programming problems (MIWCPP) consisting of minimizing a difference of a quadratic function and a convex function. A new necessary global optimality conditions for MIWCPP is presented in this paper. A new local optimization method for MIWCPP is designed based on the necessary global optimality conditions, which is different from the traditional local optimization method. A global optimization method is proposed by combining some auxiliary functions and the new local optimization method. Furthermore, numerical examples are also presented to show that the proposed global optimization method for MIWCPP is efficient.