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101.
W. W. Hager P. M. Pardalos I. M. Roussos H. D. Sahinoglou 《Journal of Optimization Theory and Applications》1991,68(3):499-511
The observation that at leasts constraints are active when the Hessian of the Lagrangian hass negative eigenvalues at a local minimizer is used to obtain two results: (i) a class of nearly concave quadratic minimization problem can be solved in polynomial time; (ii) a class of indefinite quadratic test problems can be constructed with a specified number of positive and negative eigenvalues and with a known global minimizer.The authors thank the reviewers for their constructive comments. The first author was supported by the National Science Foundation Grant DMS-85-20926 and by the Air Force Office of Scientific Research Grant AFOSR-ISSA-86-0091. 相似文献
102.
A chance constrained stochastic program is considered that arises from an application to college enrollments and in which the objective function is the expectation of a linear function of the random variables. When these random variables are independent and normally distributed with mean and variance that are linear in the decision variables, the deterministic equivalent of the problem is a nonconvex nonlinear knapsack problem. The optimal solution to this problem is characterized and a greedy-type heuristic algorithm that exploits this structure is employed. Computational results show that the algorithm performs well, especially when the normal random variables are approximations of binomial random variables. 相似文献
103.
We study the problem of scheduling n non-preemptable jobs on a single machine which is not available for processing during a given time period. The objective is to minimize the sum of the job completion times. The best known approximation algorithm for this NP-hard problem has a relative worst-case error bound of 17.6%. We present a parametric O(nlog n)-algorithm H with which better worst-case error bounds can be obtained. The best error bound calculated for the algorithm in the paper is 7.4%. In a computational experiment, we test the algorithm with the performance guarantee set to 10.2%. It turns out that randomly generated instances with up to 1000 jobs can be solved with a mean (maximum) error of 0.31% (3.18%) and a mean (maximum) computation time of 0.8 (9.7) seconds. 相似文献
104.
105.
S. Prestwich 《Annals of Operations Research》2003,118(1-4):137-150
Symmetries occur in many combinatorial problems, and a great deal of research has been done on symmetry breaking techniques for backtrack search. However, few results have been reported on the use of symmetry breaking with local search. On four classes of problem we find that adding symmetry breaking constraints to a model impairs local search performance, in terms of both execution time and search steps. We also find that implied constraints can impair backtrack search performance. These results show that modeling techniques and search heuristics should be combined with caution. They also motivate a novel modeling technique for local search: removing constraints to add new symmetries. 相似文献
106.
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
107.
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
108.
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
109.
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
110.
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