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 condi...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.展开更多
In this paper,firstly,we give a counterexample to point out there exist deficiencies in our previous works(Wu et al.in J Glob Optim 31:45-60,2005).In addition,we improve the corresponding results.Finally,an example is...In this paper,firstly,we give a counterexample to point out there exist deficiencies in our previous works(Wu et al.in J Glob Optim 31:45-60,2005).In addition,we improve the corresponding results.Finally,an example is presented to illustrate how a monotone non-convex optimization problem can be transformed into an equivalent convex minimization problem.展开更多
In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optim...In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.展开更多
基金supported by Natural Science Foundation of Chongqing(Nos.cstc2013jjB00001 and cstc2011jjA00010).
文摘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.
基金founded by the National Natural Science Foundation of China(Nos.11991024,11871128,and 11771064).
文摘In this paper,firstly,we give a counterexample to point out there exist deficiencies in our previous works(Wu et al.in J Glob Optim 31:45-60,2005).In addition,we improve the corresponding results.Finally,an example is presented to illustrate how a monotone non-convex optimization problem can be transformed into an equivalent convex minimization problem.
基金the National Natural Science Foundation of China(No.11471062).
文摘In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.
