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131.
In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising. 相似文献
132.
The asymptotic behavior of state-constrained semilinear optimal control problems for distributed-parameter systems with variable
compact control zones is investigated. We derive conditions under which the limiting problems can be made explicit.
We gratefully acknowledge the support of the DAAD. The paper was prepared during the visit of the first author at the Institute
of Applied Mathematics II, University Erlangen-Nuremberg in 2003. 相似文献
133.
Z. Y. Wu V. Jeyakumar A. M. Rubinov 《Journal of Optimization Theory and Applications》2007,133(1):123-130
We present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality
constraints as well as equality constraints. By employing the Lagrangian function, we extend the global subdifferential approach,
developed recently in Jeyakumar et al. (J. Glob. Optim., 2007, to appear; Math. Program. Ser. A, 2007, to appear) for studying bivalent quadratic programs without quadratic constraints, and derive global optimality conditions.
The authors are grateful to the referees for constructive comments and suggestions which have contributed to the final preparation
of the paper.
Z.Y. Wu’s current address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria,
Australia. The work of this author was completed while at the Department of Applied Mathematics, University of New South Wales,
Sydney, Australia. 相似文献
134.
This paper establishes a type of Kantorovich inequality subject to some constraints and obtains some lower bounds for the relative efficiency of the least squares. These lower bounds can be much sharper than that obtained by using the unconstrained Kantorovich inequality. Multivariate extensions of the results are also obtained. Some interesting examples are presented. 相似文献
135.
An interior-point affine-scaling trust-region method for semismooth equations with box constraints 总被引:1,自引:0,他引:1
An algorithm for the solution of a semismooth system of equations with box constraints is described. The method is an affine-scaling
trust-region method. All iterates generated by this method are strictly feasible. In this way, possible domain violations
outside or on the boundary of the box are avoided. The method is shown to have strong global and local convergence properties
under suitable assumptions, in particular, when the method is used with a special scaling matrix. Numerical results are presented
for a number of problems arising from different areas. 相似文献
136.
A. V. Arutyunov D. Yu. Karamzin 《Computational Mathematics and Mathematical Physics》2007,47(3):349-360
The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results. 相似文献
137.
S. Ramasubramanian 《Applied Mathematics and Optimization》2007,56(3):312-342
We consider a network of d companies (insurance companies, for example) operating under a treaty to diversify risk. Internal and external borrowing
are allowed to avert ruin of any member of the network. The amount borrowed to prevent ruin is viewed upon as control. Repayment
of these loans entails a control cost in addition to the usual costs. Each company tries to minimize its repayment liability.
This leads to a d -person differential game with state space constraints. If the companies are also in possible competition a Nash equilibrium
is sought. Otherwise a utopian equilibrium is more appropriate. The corresponding systems of HJB equations and boundary conditions
are derived. In the case of Nash equilibrium, the Hamiltonian can be discontinuous; there are d interlinked control problems with state constraints; each value function is a constrained viscosity solution to the appropriate
discontinuous HJB equation. Uniqueness does not hold in general in this case. In the case of utopian equilibrium, each value
function turns out to be the unique constrained viscosity solution to the appropriate HJB equation. Connection with Skorokhod
problem is briefly discussed. 相似文献
138.
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
139.
本文利用广义投影矩阵,对求解无约束规划的超记忆梯度算法中的参数给出一种新的取值范围以保证得到目标函数的超记忆梯度广义投影下降方向,并与处理任意初始点的方法技巧结合建立求解非线性不等式约束优化问题的一个初始点任意的超记忆梯度广义投影算法,在较弱条件下证明了算法的收敛性.同时给出结合FR,PR,HS共轭梯度参数的超记忆梯度广义投影算法,从而将经典的共轭梯度法推广用于求解约束规划问题.数值例子表明算法是有效的. 相似文献
140.
Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-known assignment problem. 相似文献