A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed....A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.展开更多
In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of s...In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.展开更多
This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonl...This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.展开更多
Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered...Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.展开更多
This paper considers the mathematical programs with equilibrium constraints(MPEC).It is well-known that,due to the existence of equilibrium constraints,the Mangasarian-Fromovitz constraint qualification does not hold ...This paper considers the mathematical programs with equilibrium constraints(MPEC).It is well-known that,due to the existence of equilibrium constraints,the Mangasarian-Fromovitz constraint qualification does not hold at any feasible point of MPEC and hence,in general,the developed numerical algorithms for standard nonlinear programming problems can not be applied to solve MPEC directly.During the past two decades,much research has been done to develop numerical algorithms and study optimality,stability,and sensitivity for MPEC.However,there are very few results on duality for MPEC in the literature.In this paper,we present a Wolfe-type duality for MPEC and,under some suitable conditions,we establish various duality theorems such as the weak duality,direct duality,converse duality,and strict converse duality theorems.We further show that a linear MPEC is equivalent to a linear programming problem in some sense.展开更多
文中提出一种智能电网环境下可控负荷优化调度的双层优化模型。上层是可控负荷聚合器的优化问题,其目标是通过优化调度3类可控负荷的方式最小化购电成本;下层是电网优化问题,该问题提供电网实时电价给上层优化问题。文中将电网优化问题...文中提出一种智能电网环境下可控负荷优化调度的双层优化模型。上层是可控负荷聚合器的优化问题,其目标是通过优化调度3类可控负荷的方式最小化购电成本;下层是电网优化问题,该问题提供电网实时电价给上层优化问题。文中将电网优化问题的KKT条件作为可控负荷优化问题的均衡约束,双层优化问题转换为具有均衡约束的数学规划(Mathematical Program with Equilibrium Constraints,MPEC)问题来求解。算例仿真反映了提出的调度策略的基本特征。展开更多
基金project supported by the National Natural Science Foundation of China(Nos.10501009 and 60471039)the Natural Science Foundation of Guangxi Province(No.0728206)
文摘A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.
基金supported by the National Natural Science Foundation of China (Nos.10501009,10771040)the Natural Science Foundation of Guangxi Province of China (Nos.0728206,0640001)the China Postdoctoral Science Foundation (No.20070410228)
文摘In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.
文摘This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.
文摘Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.
基金supported by the NSFC Grant(No.11401379)supported in part by the NSFC Grant(No.11431004)the China Postdoctoral Science Foundation(No.2014M550237)
文摘This paper considers the mathematical programs with equilibrium constraints(MPEC).It is well-known that,due to the existence of equilibrium constraints,the Mangasarian-Fromovitz constraint qualification does not hold at any feasible point of MPEC and hence,in general,the developed numerical algorithms for standard nonlinear programming problems can not be applied to solve MPEC directly.During the past two decades,much research has been done to develop numerical algorithms and study optimality,stability,and sensitivity for MPEC.However,there are very few results on duality for MPEC in the literature.In this paper,we present a Wolfe-type duality for MPEC and,under some suitable conditions,we establish various duality theorems such as the weak duality,direct duality,converse duality,and strict converse duality theorems.We further show that a linear MPEC is equivalent to a linear programming problem in some sense.
文摘文中提出一种智能电网环境下可控负荷优化调度的双层优化模型。上层是可控负荷聚合器的优化问题,其目标是通过优化调度3类可控负荷的方式最小化购电成本;下层是电网优化问题,该问题提供电网实时电价给上层优化问题。文中将电网优化问题的KKT条件作为可控负荷优化问题的均衡约束,双层优化问题转换为具有均衡约束的数学规划(Mathematical Program with Equilibrium Constraints,MPEC)问题来求解。算例仿真反映了提出的调度策略的基本特征。
