Efficient algorithms for solving rank two and rank three bilinear programming problems

Finitely convergent algorithms for solving rank two and three bilinear programming problems are proposed. A rank k bilinear programming problem is a nonconvex quadratic programming problem with the following structure: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaacaWFTbGaa8% xAaiaa-5gacaWFPbGaa8xBaiaa-LgacaWF6bGaa8xzaiaa-bcacaWF% 7bacbiGaa43yamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+Hhaca% GFRaGaa4hzamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+LhacaGF% RaWaaabuaeaacaGFJbWaa0baaSqaaiaa+PgaaeaacaGF0baaaOGaam% iEaiabl+y6NjaadsgadaqhaaWcbaGaamOAaaqaaiaadshaaaGccaWG% 5bGaaiiFaaWcbaGaa8NAaiaa-1dacaWFXaaabeqdcqGHris5aOGaa4% hEaiabgIGiolaa+HfacaGFSaGaa4xEaiabgIGiolaa+LfacaWF9bGa% a8hlaaaa!5D2E!\[minimize \{ c_0^t x + d_0^t y + \sum\limits_{j = 1} {c_j^t xd_j^t y|} x \in X,y \in Y\} ,\]where X Rⁿ¹ and Y R ⁿ² are non-empty and bounded polytopes. We show that a variant of parametric simplex algorithm can solve large scale rank two bilinear programming problems efficiently. Also, we show that a cutting-cake algorithm, a more elaborate variant of parametric simplex algorithm can solve medium scale rank three problems.This research was supported in part by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. 63490010.     

Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison

We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b]. Problem P: find a globally-optimal value off and a corresponding point; Problem Q: find a set of disjoint subintervals of [a, b] containing only points with a globally-optimal value and the union of which contains all globally optimal points. A two-phase algorithm is proposed for Problem P. In phase I, this algorithm obtains rapidly a solution which is often globally-optimal. Moreover, a sufficient condition onf for this to be the case is given. In phase II, the algorithm proves the-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globally-optimal value. The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen. For small, the new algorithm requires only a few percent more function evaluations than the best possible one. An extended version of Piyavskii's algorithm is proposed for problem Q. A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals. This result is achieved for all twenty test problems.The research of the authors has been supported by AFOSR grants 0271 and 0066 to Rutgers University. Research of the second author has been also supported by NSERC grant GP0036426, FCAR grant 89EQ4144 and partially by AFOSR grant 0066. We thank Nicole Paradis for her help in drawing the figures.     

On affine scaling algorithms for nonconvex quadratic programming

We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.     

Chemical Bonding and Pressure‐Induced Change of the Electron Configuration of Ytterbium in β‐YbAgGa2

Single‐phase polycrystalline samples of the intermetallic compound β‐YbAgGa₂ were synthesized by inductive heating and subsequent annealing for eight weeks at 670 K. Magnetic properties were characterized by susceptibility measurements and indicated intermediate valence of ytterbium at ambient pressure. Angle‐dispersive X‐ray powder diffraction data of orthorhombic β‐YbAgGa₂ indicate stability of the phase in the investigated pressure range from 0.1 MPa (ambient pressure) to 19 GPa. The pressure‐induced volume decrease is accompanied by an increase of the effective valence from 2.17 at ambient conditions to 2.71 at 16 GPa as evaluated by X‐ray absorption spectroscopy at the Yb L_III threshold. Analysis of the chemical bonding in β‐YbAgGa₂ by integrating the electron density of the polyanion in basins as defined by the electron localization function results in an electron count Yb^2.7+[(Ag^0.2—)(Ga1(3b)^1.0—)(Ga2(4b)^1.5—)]. This finding is close to the expected values calculated by means of the Zintl rules and fits well the results of magnetic susceptibility measurements and XAS investigations.     

The chemical bond in polyphosphides: crystal structures, the electron localization function, and a new view of aromaticity in P4(2-) and P5(-)

The incongruent solvation of M(I)4P6 species (M(I) = K, Rb, Cs) in liquid ammonia leads to a broad variety of polyphosphides such as P7(3-), P11(3-), and the putatively aromatic P4(2-) and P5(-), which we investigated by using NMR spectroscopy and single-crystal X-ray structure analysis. The structures of Cs2P4 x 2 NH3, (K@[18]crown-6)3K3(P7)2 x 10 NH3, Rb3P7 x 7 NH3, and (Rb@[18]crown-6)3P7 x 6 NH3 are discussed and compared. The electron localization function ELF is used in a comparison of the chemical bonding of various phosphorus species. The variances of the basin populations provide a well-established measure for electron delocalization and therefore aromaticity. While comparable variance is calculated for P4(2-) and P5(-) it is observed in the lone pairs rather than in the basin populations of the bonds as in the prototypical aromatic hydrocarbons such as benzene or the cyclopentadienide anion. For this behavior, the term "lone pair aromaticity" is proposed.     

基于流量测点的热网变动阻力系数优化辨识

随着供热计量系统的普及,系统可以根据负荷的变化进行调整,管网的阻力系数随即发生变化.对变动阻力系数进行优化辨识是了解供热管网实时运行状况的有效手段.提出一种基于流量监测数据的供热管网变动阻力系数优化辨识方法,并利用遗传算法进行求解.对洛阳市某小区供暖季管网实际运行数据进行验证,辨识结果的相对误差在5％以内.结果表明:该...     

An Algorithm Framework for Drug-Induced Liver Injury Prediction Based on Genetic Algorithm and Ensemble Learning

In the process of drug discovery, drug-induced liver injury (DILI) is still an active research field and is one of the most common and important issues in toxicity evaluation research. It directly leads to the high wear attrition of the drug. At present, there are a variety of computer algorithms based on molecular representations to predict DILI. It is found that a single molecular representation method is insufficient to complete the task of toxicity prediction, and multiple molecular fingerprint fusion methods have been used as model input. In order to solve the problem of high dimensional and unbalanced DILI prediction data, this paper integrates existing datasets and designs a new algorithm framework, Rotation-Ensemble-GA (R-E-GA). The main idea is to find a feature subset with better predictive performance after rotating the fusion vector of high-dimensional molecular representation in the feature space. Then, an Adaboost-type ensemble learning method is integrated into R-E-GA to improve the prediction accuracy. The experimental results show that the performance of R-E-GA is better than other state-of-art algorithms including ensemble learning-based and graph neural network-based methods. Through five-fold cross-validation, the R-E-GA obtains an ACC of 0.77, an F1 score of 0.769, and an AUC of 0.842.     

Modified Wave Particle Duality and Black Hole Physics

de Broglie relation is revisited, in consideration of a generalization of canonical commuting relation. The possible effects on particle's localization and black hole physics are also discussed, in a heuristic manner.     

遗传算法优化变分模态分解提取舰船辐射噪声特征线谱方法

特征线谱提取是舰船目标识别的一个重要研究环节,常采用传统的DEMON谱分析方法,处理过程中,一般对舰船噪声时域信号未予抑噪,低信噪比情况下,传统DEMON谱分析性能差。对此,提出一种采用遗传算法优化变分模态分解方法,用于分解舰船噪声原时域信号,获得抑制噪声后的舰船噪声重构信号,进而有效提取了舰船目标噪声幅度调制特征线谱。该方法首先采用遗传算法优化变分模态分解的两个关键输入参数(分解所取模态个数和惩罚因子),对变分模态分解得到的各阶固有模态分量加以判别,去除噪声主导分量,保留信号主导分量,使重构舰船噪声信号显著抑制了干扰噪声,然后对降噪后的重构信号进行频谱分析,获得目标噪声调制特征线谱。理论分析、仿真和实验数据处理结果表明,相比传统DEMON谱分析法,基于遗传算法优化变分模态分解的舰船噪声特征线谱提取方法具有更好的噪声抑制能力,所获取的舰船噪声幅度调制特征线谱信噪比明显高于传统DEMON方法,具有一定优势,前景良好。     

A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

A newly-developed numerical algorithm, which is called the new Generalized-α (G-α) method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero-stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.The English text was polished by Keren Wang.