Hybrid extragradient proximal algorithm coupled with parametric approximation and penalty/barrier methods

In this article we study the hybrid extragradient method coupled with approximation and penalty schemes for convex minimization problems. Under certain hypotheses, which include, for example, the case of Tikhonov regularization, we prove asymptotic convergence of the method to the solution set of our minimization problem. When we use schemes of penalization or barrier, we can show asymptotic convergence using the well-known fast/slow parameterization techniques and exploiting the existence and finite length of an optimal path.     

On the decay of solutions for a class of quasilinear hyperbolic equations with non‐linear damping and source terms

In this paper, we consider the non‐linear wave equation a,b>0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on α, m, and p, we give precise decay rates for the solution. In particular, we show that for m=0, the decay is exponential. This work improves the result by Yang (Math. Meth. Appl. Sci. 2002; 25 :795–814). Copyright © 2005 John Wiley & Sons, Ltd.     

基于比率的三种群混合扩散模型的动力学行为

讨论了一类基于比率的非自治三种群混合扩散模型,三种群间既有捕食关系又有竞争关系.我们研究了该模型的动力学行为:包括一致持久性,全局渐近稳定性,周期解,概周期解的存在唯一性.表明即使食饵种群在某些孤立的斑块中可能绝灭,也可以通过适当选取扩散率来保证系统持续生存.     

二次概周期系数微分方程的概周期解

利用指数二分性,Schauder不动点定理和Grownwall不等式证明了一类概周期系数微分方程的概周期解、有界解的存在唯一性及概周期解的全局吸引性.     

PERMANENCE AND GLOBAL STABILITY OF A FEEDBACK CONTROL SYSTEM WITH DELAYS

This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by constructing a suitable Lyapunov functional, a criterion for the global stability of the model is obtained.     

Investigation of nanostructured Fe3O4 polypyrrole core-shell composites by X-ray absorbtion spectroscopy and X-ray diffraction using synchrotron radiation

In this article, we focus on the structural peculiarities of nanosized Fe₃O₄ in the core-shell nanocomposites obtained by polymerization of conducting polypyrrole shell around Fe₃O₄ nanoparticles. The local structure of Fe atoms was determined from the Extended X-ray Absorption Fine Structure analysis using our own package computer programs. An X-ray diffraction method that is capable to determine average particle size, microstrains, as the particle size distribution of Fe₃O₄ nanoparticles is presented. The method is based on the Fourier analysis of a single X-ray diffraction profile using a new fitting method based on the generalized Fermi function facilities. The crystallites size obtained by X-ray diffraction spectra analysis was estimated between 3.2 and 10.3 nm. Significant changes in the first and the second Fe coordination shell in comparison with standard bulk were observed. The global and local structure of the nanosized Fe₃O₄ are correlated with the synthesis conditions of the core-shell polypyrrole nanocomposites.     

Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Complete Solutions and Extremality Criteria to Polynomial Optimization Problems

This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (2000), Duality Principles in Nonconvex Systems: Theory, Method and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + 454 pp], the nonconvex polynomials in can be converted into an one-dimensional canonical dual optimization problem, which can be solved completely. Therefore, a set of complete solutions to the original problem is obtained. Both global minimizer and local extrema of certain special polynomials can be indentified by Gao-Strang’s gap function and triality theory. For general nonconvex polynomial minimization problems, a sufficient condition is proposed to identify global minimizer. Applications are illustrated by several examples.     

Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.     

Unipotent Algebraic Affine Supergroups and Nilpotent Lie Superalgebras

We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras, regarded as coalgebras, is also discussed. Presented by S. Montgomery Mathematics Subject Classification (2000) 16W30.