6,670 research outputs found
Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix
Cross-efficiency evaluation method is an effective and widespread adopted data envelopment analysis (DEA) method with self-assessment and peer-assessment to evaluate and rank decision making units (DMUs). Extant aggressive, benevolent, and neutral cross-efficiency methods are used to evaluate DMUs with competitive, cooperative, and nontendentious relationships, respectively. In this paper, a symmetric (nonsymmetric) compete-cooperate matrix is introduced into aggressive and benevolent cross-efficiency methods and compete-cooperate cross-efficiency method is proposed to evaluate DMUs with diverse (relative) relationships. Deviation maximization method is applied to determine the final weights of cross-evaluation to enhance the differentiation ability of cross-efficiency evaluation method. Numerical demonstration is provided to illustrate the reasonability and practicability of the proposed method
High-order symbolic strong-coupling expansion for the Bose-Hubbard model
Combining the process-chain method with a symbolized evaluation we work out
in detail a high-order symbolic strong-coupling expansion (HSSCE) for
determining the quantum phase boundaries between the Mott insulator and the
superfluid phase of the Bose-Hubbard model for different fillings in hypercubic
lattices of different dimensions. With a subsequent Pad{\'e} approximation we
achieve for the quantum phase boundaries a high accuracy, which is comparable
to high-precision quantum Monte-Carlo simulations, and show that all the Mott
lobes can be rescaled to a single one. As a further cross-check, we find that
the HSSCE results coincide with a hopping expansion of the quantum phase
boundaries, which follow from the effective potential Landau theory (EPLT).Comment: 15 pages, 11 figures. For the latest version and more information see
https://www.physik.uni-kl.de/eggert/papers/index.htm
Global Optimization for a Class of Nonlinear Sum of Ratios Problem
We present a branch and bound algorithm for globally solving the sum of ratios problem. In this problem, each term in the objective function is a ratio of two functions which are the sums of the absolute values of affine functions with coefficients. This problem has an important application in financial optimization, but the global optimization algorithm for this problem is still rare in the literature so far. In the algorithm we presented, the branch and bound search undertaken by the algorithm uses rectangular partitioning and takes place in a space which typically has a much smaller dimension than the space to which the decision variables of this problem belong. Convergence of the algorithm is shown. At last, some numerical examples are given to vindicate our conclusions
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