共查询到20条相似文献,搜索用时 109 毫秒
1.
2.
本文研究了非线性互补的光滑化问题.利用一个新的光滑NCP函数将非线性互补问题转化为等价的光滑方程组,并在此基础上建立了求解P0-函数非线性互补问题的一个完全光滑化牛顿法,获得了算法的全局收敛性和局部二次收敛性的结果.并给出数值实验验证了理论分析的正确性. 相似文献
3.
4.
5.
6.
非线性互补问题(NCP)可以重新表述为一个非光滑方程组的解.通过引入一个新的光滑函数,将问题近似为参数化光滑方程组.基于这个光滑函数,我们提出了一个求解P0映射和R0映射非线性互补问题的光滑牛顿法.该算法每次迭代只求解一个线性方程和一次线搜索.在适当的条件下,证明了该方法是全局和局部二次收敛的.数值结果表明,该算法是有效的. 相似文献
7.
本文构造了非线性互补问题一个新的光滑逼近函数,分析了该函数的一些基本性质.利用这一新的光滑逼近函数建立了求解非线性互补问题的一个Jacobi光滑化方法,并证明了在适当的条件下这一算法是全局及局部超线性收敛的.数值结果表明该方法是有效的. 相似文献
8.
提出了—个求解非线性互补约束均衡问题的滤子SQP算法.借助Fischer-Burmeister函数把均衡约束转化为—个非光滑方程组,然后利用逐步逼近和分裂思想,给出—个与原问题近似的一般的约束优化.引入滤子思想,避免了罚函数法在选择罚因子上的困难.在适当的条件下证明了算法的全局收敛性,部分的数值结果表明算法是有效的. 相似文献
9.
10.
11.
12.
J. J. Júdice H. D. Sherali I. M. Ribeiro A. M. Faustino 《Journal of Optimization Theory and Applications》2007,134(3):467-481
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
13.
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
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
14.
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
15.
16.
<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
17.
A new formulation as well as a new solution technique is proposed for an equilibrium path-following method in two-dimensional quasistatic frictional contact problems. We consider the Coulomb friction law as well as a geometrical nonlinearity explicitly. Based on a criterion of maximum dissipation of energy, we propose a formulation as a mathematical program with complementarity constraints (MPEC) in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPEC is proposed, which can be solved by using a conventional nonlinear programming approach. The equilibrium paths of various structures are computed in cases such that there exist some limit points and/or infinite number of successive bifurcation points. 相似文献
18.
We propose a merit-function piecewise SQP algorithm for mathematical programs with equilibrium constraints (MPEC) formulated
as mathematical programs with complementarity constraints. Under mild conditions, the new algorithm is globally convergent
to a piecewise stationary point. Moreover, if the partial MPEC linear independence constraint qualification (LICQ) is satisfied
at the accumulation point, then the accumulation point is an S-stationary point.
The research of the first author was supported by the National Natural Science Foundation of China under grants 10571177 and
70271014. The research of the second author was partially supported by NSERC. 相似文献
19.
C. Ling L. Q. Qi G. L. Zhou S. Y. Wu 《Journal of Optimization Theory and Applications》2006,129(1):147-164
The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth
nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the
integral function, gradient-based algorithms cannot be used to solve this nonsmooth nonlinear programming problem. To overcome
this difficulty, we present a robust smoothing sequential quadratic programming (SQP) algorithm for solving the nonsmooth
nonlinear programming problem. At each iteration of the algorthm, we need to solve only a quadratic program that is always
feasible and solvable. The global convergence of the algorithm is established under mild conditions. Numerical results are
given.
Communicated by F. Giannessi
His work was supported by the Hong Kong Research Grant Council
His work was supported by the Australian Research Council. 相似文献
20.
We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are all weaker than the MPEC linear independence constraint qualification, and derive several second-order optimality conditions for MPEC under the new MPEC constraint qualifications. Finally, we discuss the isolatedness of local minimizers for MPEC under very weak conditions. 相似文献