首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 125 毫秒
1.
本文讨论了非线性等式与不等式约束的优化问题的一族比较广的精确罚函数的存在性,不需凸性及任何约束规格的假设,证明了当罚参数充分大后,惩罚问题的(严格)局部极小点是原问题的(严格)局部极小点,惩罚问题的全局极小点是原问题的最优解,并给出控制参数的一个下界。  相似文献   

2.
针对等式及不等式约束极小化问题,通过对原问题添加一个变量,给出一个新的简单精确罚函数,即在该精确罚函数表达式中,不含有目标函数及约束函数的梯度.在满足某些约束品性的条件下,可以证明:当罚参数充分大时,所给出的罚问题的局部极小点是原问题的局部极小点.  相似文献   

3.
求解一类MPEC问题的一种UV -分解方法   总被引:1,自引:1,他引:0  
给出了求解具有线性互补约束的MPEC问题的一种UV -分解方法.首先将MPEC问题化为非线性规划问题,给出一种相应的罚函数的次微分结构及其UV -分解的结果,根据所得到的结果构造一个具有超线性收敛速度的概念型算法.  相似文献   

4.
一种新的求解带约束的有限极大极小问题的精确罚函数   总被引:1,自引:0,他引:1  
提出了一种新的精确光滑罚函数求解带约束的极大极小问题.仅仅添加一个额外的变量,利用这个精确光滑罚函数,将带约束的极大极小问题转化为无约束优化问题.证明了在合理的假设条件下,当罚参数充分大,罚问题的极小值点就是原问题的极小值点.进一步,研究了局部精确性质.数值结果表明这种罚函数算法是求解带约束有限极大极小问题的一种有效算法.  相似文献   

5.
针对混合整数非线性约束优化问题(MINLP)的一般形式,通过罚函数的方法,给出了它的几种等价形式,并证明了最优解的等价性.将约束优化问题转化成更容易求解的无约束非线性优化问题,并把混合整数规划转化成非整数优化问题,从而将MINLP的求解简化为求解一个连续的无约束非线性优化问题,进而可用已有的一般无约束优化算法进行求解.  相似文献   

6.
本文通过给出的一个修正的罚函数,把约束非线性规划问题转化为无约束非线性规划问题.我们讨论了原问题与相应的罚问题局部最优解和全局最优解之间的关系,并给出了乘子参数和罚参数与迭代点之间的关系,最后给出了一个简单算法,数值试验表明算法是有效的.  相似文献   

7.
本文把战斗对策归结为有约束极小极大问题,讨论解的存在性.引进不连续罚函数后,把有约束问题化为无约束极小极大问题。  相似文献   

8.
针对可微非线性规划问题提出了一个新的逼近精确罚函数的罚函数形式,给出了近似逼近算法与渐进算法,并证明了近似算法所得序列若有聚点,则必为原问题最优解. 在较弱的假设条件下,证明了算法所得的极小点列有界,且其聚点均为原问题的最优解,并得到在Mangasarian-Fromovitz约束条件下,经过有限次迭代所得的极小点为可行点.  相似文献   

9.
全局优化是最优化的一个分支,非线性整数规划问题的全局优化在各个方面都有广泛的应用.填充函数是解决全局优化问题的方法之一,它可以帮助目标函数跳出当前的局部极小点找到下一个更好的极小点.滤子方法的引入可以使得目标函数和填充函数共同下降,省却了以往算法要设置两个循环的麻烦,提高了算法的效率.本文提出了一个求解无约束非线性整数规划问题的无参数填充函数,并分析了其性质.同时引进了滤子方法,在此基础上设计了整数规划的无参数滤子填充函数算法.数值实验证明该算法是有效的.  相似文献   

10.
解决有约束非线性规划问题的一个基本方法足将之简化为无约束问题,比如罚函数法.其中精确罚函数法是通过解决某个无约束问题来获得原有约束问题的一个解.就经典的罚函数定义而言,简单精确罚函数是非光滑的,从而难以处理.作者提出一个简单光滑精确指数乘子罚函数,验证在二阶充分条件下它存在相应的超线性收敛率,并得到关于它的强弱对偶结果.  相似文献   

11.
提出了一种易实施的求无约束不可微规划的信赖域算法,并在一定条件下证明了该算法所产生的点列的任何聚点都是原问题的稳定点。  相似文献   

12.
欧宜贵  侯定丕 《数学杂志》2003,23(3):345-348
本文提出了一个易实施的处理一类无约束复合非光滑优化的信赖域算法,并在一定条件下证明了该算法所产生的迭代序列的任何聚点都是原问题的稳定点.  相似文献   

13.
In this paper, an algorithm for solving a mathematical programming problem with complementarity (or equilibrium) constraints (MPEC) is introduced, which uses the active-set methodology while maintaining the complementarity restrictions throughout the procedure. Finite convergence of the algorithm to a strongly stationary point of the MPEC is established under reasonable hypotheses. The algorithm can be easily implemented by adopting any active-set code for nonlinear programming. Computational experience is included to highlight the efficacy of the proposed method in practice.  相似文献   

14.
<正>Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.  相似文献   

15.
In this paper an exterior point polynomial time algorithm for convex quadratic programming problems is proposed. We convert a convex quadratic program into an unconstrained convex program problem with a self-concordant objective function. We show that, only with duality, the Path-following method is valid. The computational complexity analysis of the algorithm is given.  相似文献   

16.
With the aid of some novel complementarity constraint qualifications, we derive some simplified primal-dual characterizations of a B-stationary point for a mathematical program with complementarity constraints (MPEC). The approach is based on a locally equivalent piecewise formulation of such a program near a feasible point. The simplified results, which rely heavily on a careful dissection and improved understanding of the tangent cone of the feasible region of the program, bypass the combinatorial characterization that is intrinsic to B-stationarity.  相似文献   

17.
求解带均衡约束数学规划问题的一个连续化方法   总被引:3,自引:0,他引:3  
李飞  徐成贤 《计算数学》2004,26(1):3-12
In this paper, a continuation method for mathematical programs with equilibrium constraints (MPEC) is proposed. By using the KKT conditions for the variational inequality constraints, the MPEC is firstly reformulated as a nonsmooth constrained optimization problem, then we solve a sequence of smooth perturbation problems, which progressively approximate the nonsmooth problem, and study the convergence of the proposed method. Numerical results showing feasibility of the approach are given.  相似文献   

18.
It is well known that mathematical programs with equilibrium constraints (MPEC) violate the standard constraint qualifications such as Mangasarian–Fromovitz constraint qualification (MFCQ) and hence the usual Karush–Kuhn–Tucker conditions cannot be used as stationary conditions unless relatively strong assumptions are satisfied. This observation has led to a number of weaker stationary conditions, with Mordukhovich stationary (M-stationary) condition being the strongest among the weaker conditions. In nonlinear programming, it is known that MFCQ leads to an exact penalization. In this paper we show that MPEC GMFCQ, an MPEC variant of MFCQ, leads to a partial exact penalty where all the constraints except a simple linear complementarity constraint are moved to the objective function. The partial exact penalty function, however, is nonsmooth. By smoothing the partial exact penalty function, we design an algorithm which is shown to be globally convergent to an M-stationary point under an extended version of the MPEC GMFCQ.  相似文献   

19.
陈风华  李双安 《数学杂志》2015,35(2):429-442
本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号