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81.
M. V. Dolgopolik 《Optimization》2017,66(10):1577-1622
In this article, we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be both smooth and exact unlike the standard (i.e. non-parametric) exact penalty functions that are always nonsmooth. We obtain several necessary and/or sufficient conditions for the exactness of parametric penalty functions, and for the zero duality gap property to hold true for these functions. We also prove some convergence results for the method of parametric penalty functions, and derive necessary and sufficient conditions for a parametric penalty function to not have any stationary points outside the set of feasible points of the constrained optimization problem under consideration. In the second part of the paper, we apply the general theory of exact parametric penalty functions to a class of parametric penalty functions introduced by Huyer and Neumaier, and to smoothing approximations of nonsmooth exact penalty functions. The general approach adopted in this article allowed us to unify and significantly sharpen many existing results on parametric penalty functions. 相似文献
82.
83.
We consider random subgraphs of a fixed graph with large minimum degree. We fix a positive integer k and let Gk be the random subgraph where each independently chooses k random neighbors, making kn edges in all. When the minimum degree then Gk is k‐connected w.h.p. for ; Hamiltonian for k sufficiently large. When , then Gk has a cycle of length for . By w.h.p. we mean that the probability of non‐occurrence can be bounded by a function (or ) where . © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 143–157, 2017 相似文献
84.
85.
The Hamilton–Waterloo problem asks for a 2‐factorization of (for v odd) or minus a 1‐factor (for v even) into ‐factors and ‐factors. We completely solve the Hamilton–Waterloo problem in the case of C3‐factors and ‐factors for . 相似文献
86.
In this paper, we extend one of Erdélyi's classical integrals for the Gauss hypergeometric functions to a special class of generalized hypergeometric functions in which certain pairs of numerator and denomiator parameters differ by positive integers. Our main results are achieved by applying the fractional integration by parts and series manipulation technique. Some special cases are also pointed out which includes a new extension of a Thomae-type transformation. 相似文献
87.
Mostafa M.A. Khater Emad H.M. Zahran Maha S.M. Shehata 《Journal of the Egyptian Mathematical Society》2017,25(1):8-12
In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota–Satsuma couple KdV system according to the modified simple equation method with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented. 相似文献
88.
The Casimir element of a fusion ring (R, B) gives rise to the so called Casimir matrix C of (R, B). This enables us to construct a generalized Cartan matrix D-C in the sense of Kac for a suitable diagonal matrix D. In this paper, we study some elementary properties of the Casimir matrix C and use them to realize certain fusion rings from the generalized Cartan matrix D-C of finite (resp. affine) type. It turns out that there exists a fusion ring with D-C being of finite (resp. affine) type if and only if D-C has only the form A2 (resp. A1(1). We also realize all fusion rings with D-C being a particular generalized Cartan matrix of indefinite type. 相似文献
89.
The generalized T2 chart (GT‐chart), which is composed of the T2 statistic based on a small number of principal components and the remaining components, is a popular alternative to the traditional Hotelling's T2 control chart. However, the application of the GT‐chart to high‐dimensional data, which are now ubiquitous, encounters difficulties from high dimensionality similar to other multivariate procedures. The sample principal components and their eigenvalues do not consistently estimate the population values, and the GT‐chart relying on them is also inconsistent in estimating the control limits. In this paper, we investigate the effects of high dimensionality on the GT‐chart and then propose a corrected GT‐chart using the recent results of random matrix theory for the spiked covariance model. We numerically show that the corrected GT‐chart exhibits superior performance compared to the existing methods, including the GT‐chart and Hotelling's T2 control chart, under various high‐dimensional cases. Finally, we apply the proposed corrected GT‐chart to monitor chemical processes introduced in the literature. 相似文献
90.
Vicenţiu D. Rădulescu Gelson C. G. dos Santos Leandro S. Tavares 《Mathematische Nachrichten》2023,296(6):2555-2574
This paper is concerned with the existence and multiplicity of solutions for a class of problems involving the Φ-Laplacian operator with general assumptions on the nonlinearities, which include both semipositone cases and critical concave convex problems. The research is based on the subsupersolution technique combined with a truncation argument and an application of the Mountain Pass Theorem. The results in this paper improve and complement some recent contributions to this field. 相似文献