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,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
In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each i...In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each iteration point is selected from some randomly generated trial points according to certain criteria.A restarting strategy is adopted to build the restarting version of the algorithm.The performance of the presented algorithm and its restarting version are tested on 13 standard numerical examples.The numerical results suggest that the algorithm and its restarting version are very effective.展开更多
In this paper,we propose a partially parallel prediction-correction splitting method for solving block-separable linearly constrained convex optimization problems with three blocks.Unlike the extended alternating dire...In this paper,we propose a partially parallel prediction-correction splitting method for solving block-separable linearly constrained convex optimization problems with three blocks.Unlike the extended alternating direction method of multipliers,the last two subproblems in the prediction step are solved parallelly,and a correction step is employed in the method to correct the dual variable and two blocks of the primal variables.The step size adapted in the correction step allows for major contribution from the latest solution point to the iteration point.Some numerical results are reported to show the effectiveness of the presented method.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.
文摘In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each iteration point is selected from some randomly generated trial points according to certain criteria.A restarting strategy is adopted to build the restarting version of the algorithm.The performance of the presented algorithm and its restarting version are tested on 13 standard numerical examples.The numerical results suggest that the algorithm and its restarting version are very effective.
文摘In this paper,we propose a partially parallel prediction-correction splitting method for solving block-separable linearly constrained convex optimization problems with three blocks.Unlike the extended alternating direction method of multipliers,the last two subproblems in the prediction step are solved parallelly,and a correction step is employed in the method to correct the dual variable and two blocks of the primal variables.The step size adapted in the correction step allows for major contribution from the latest solution point to the iteration point.Some numerical results are reported to show the effectiveness of the presented method.
