Journal of the Operations Research Society of Japan

This paper addresses strong stability, in the sense of Kojima, of stationary solutions of nonlinear programs Pro with a finite number of equality constraints and one abstract convex constraint defined by the closed convex set K. It intends to extend results of our former paper that treated nonlinear programs Pro in a special case that K is the set of nonnegative symmetric matrices S_+. Firstly, it deduces properties of eigenvalues of the Euclidean projector on K. Secondly, it extends the results to programs Pro in case that the convex set K satisfies the regular boundary condition that S_+ always satisfies.

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Conjugate gradient methods are widely used for large scale unconstrained optimization problems. Most of conjugate gradient methods don't always generate a descent search direction, so the descent condition is usually assumed in the analysis and implementations. Dai and Yuan (1999) proposed a conjugate gradient method which generates a descent search direction at every iteration and converges globally to the solution if the Wolfe conditions are satisfied within the line search strategy. In this paper, we give a new conjugate gradient method based on the study of Dai and Yuan, and show that our method always produces a descent search direction and converges globally if the Wolfe conditions are satisfied. Moreover our method has the second-order curvature information with a higher precision which uses the modified secant condition proposed by Zhang, Deng and Chen (1999) and Zhang and Xu (2001). Our numerical results show that our method is very efficient for given standard test problems, if we make a good choice of a parameter included in our method.

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Fujishige proposed a polynomial-time maximum flow algorithm using maximum adjacency (MA) orderings. Computational results by Fujishige and Isotani showed that the algorithm was slower in practice than Goldberg and Tarjan's algorithm. In this paper we propose an improved version of Fujishige's algorithm using preflows. Our computational results show that the improved version is much faster than the original one in practice.

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The efficiencies of firms should be evaluated, based on their historical financial data. Here a process for evaluation is proposed. Each historical data set is reduced to a distribution function with a mean and a variance estimated by Kalman filter. Then, a stochastic efficiency model is applied to this reduced data. Then a new efficiency measure is proposed and compared with existing measures. An application is made to three kinds of firms.

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