With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the m...With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.展开更多
This paper presents a continuous method for solving binary quadratic programming problems. First, the original problem is converted into an equivalent continuous optimization problem by using NCP (Nonlinear Complement...This paper presents a continuous method for solving binary quadratic programming problems. First, the original problem is converted into an equivalent continuous optimization problem by using NCP (Nonlinear Complementarity Problem) function, which can be further carry on the smoothing processing by aggregate function. Therefore, the original combinatorial optimization problem could be transformed into a general differential nonlinear programming problem, which can be solved by mature optimization technique. Through some numerical experiments, the applicability, robustness, and solution quality of the approach are proved, which could be applied to large scale problems.展开更多
The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty fu...The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming.Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming.Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions.Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.展开更多
基金Supported by Science and Technology Foundation of China University of Mining & Technology
文摘With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.
文摘This paper presents a continuous method for solving binary quadratic programming problems. First, the original problem is converted into an equivalent continuous optimization problem by using NCP (Nonlinear Complementarity Problem) function, which can be further carry on the smoothing processing by aggregate function. Therefore, the original combinatorial optimization problem could be transformed into a general differential nonlinear programming problem, which can be solved by mature optimization technique. Through some numerical experiments, the applicability, robustness, and solution quality of the approach are proved, which could be applied to large scale problems.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271329 and 10971193
文摘The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming.Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming.Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions.Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.
