一种修正的CD共轭梯度法及其全局收敛性

求解无约束优化问题的共轭梯度法,其搜索方向的下降性往往依赖于所采用的线性搜索.将提出一种修正的CD算法,其搜索方向d_k始终满足1-1/u≤(-g_k~Td_k)/(‖g_k‖~2)≤1+1/u(u1),即算法在不依赖任何线性搜索的情况下能始终产生充分下降方向.同时,当采用精确线性搜索时,该修正的CD算法就是标准的CD共轭梯度法.在适当条件下,还证明了修正的CD算法在强Wolfe线性搜索下具有全局收敛性.最后,我们给出了相应的数值结果,说明了算法是一种有效的算法.     

Mixed Type Duality for Set-valued Optimization Problems via Higher-order Radial Epiderivatives

In this article, we introduce a notion of higher-order radial epiderivative for set-valued maps and study its properties. A generalized concept of higher-order strict minimizers in set-valued optimization is proposed as well. By virtue of the radial epiderivative, we establish a mixed dual problem, and then weak, strong, and converse duality theorems are obtained in dealing with generalized strict minimizers.     

Macro‐hybrid mixed variational two‐phase flow through fractured porous media

Macro‐hybrid mixed variational models of two‐phase flow, through fractured porous media, are analyzed at the mesoscopic and macroscopic levels. The mesoscopic models are treated in terms of nonoverlapping domain decompositions, in such a manner that the porous rock matrix system and the fracture network interact across rock–rock, rock–fracture, and fracture–fracture interfaces, with flux transmission conditions dualized. Alternatively, the models are scaled to a macroscopic level via an asymptotic process, where the width of the fractures tends to zero, and the fracture network turns out to be an interface system of one less spatial dimension, with variable high permeability. The two‐phase flow is characterized by a fractional flow dual mixed variational model. Augmented two‐field and three‐field variational reformulations are presented for regularization, internal approximations, and macro‐hybrid mixed finite element implementation. Also abstract proximal‐point penalty‐duality algorithms are derived and analyzed for parallel computing. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterizing optimal wages in principal-agent problems without using the first-order approach

The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA.     

Convergence of goal‐oriented adaptive finite element methods for nonsymmetric problems

In this article, we develop convergence theory for a class of goal‐oriented adaptive finite element algorithms for second‐order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type for Dirichlet problems involving the elliptic operator with A Lipschitz, symmetric positive definite, with b divergence‐free, and with . We first describe the problem class and review some standard facts concerning conforming finite element discretization and error‐estimate‐driven adaptive finite element methods (AFEM). We then describe a goal‐oriented variation of standard AFEM. Following the recent work of Mommer and Stevenson for symmetric problems, we establish contraction and convergence of the goal‐oriented method in the sense of the goal function. Our analysis approach is signficantly different from that of Mommer and Stevenson, combining the recent contraction frameworks developed by Cascon, Kreuzer, Nochetto, and Siebert; by Nochetto, Siebert, and Veeser; and by Holst, Tsogtgerel, and Zhu. We include numerical results, demonstrating performance of our method with standard goal‐oriented strategies on a convection problem. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 479–509, 2016     

Modulation of Multifunctional N,O,P Ligands for Enantioselective Copper‐Catalyzed Conjugate Addition of Diethylzinc and Trapping of the Zinc Enolate

In this work, we have successfully synthesized a new family of chiral Schiff base–phosphine ligands derived from chiral binaphthol (BINOL) and chiral primary amine. The controllable synthesis of a novel hexadentate and tetradentate N,O,P ligand that contains both axial and sp³‐central chirality from axial BINOL and sp³‐central primary amine led to the establishment of an efficient multifunctional N,O,P ligand for copper‐catalyzed conjugate addition of an organozinc reagent. In the asymmetric conjugate reaction of organozinc reagents to enones, the polymer‐like bimetallic multinuclear Cu? Zn complex constructed in situ was found to be substrate‐selective and a highly excellent catalyst for diethylzinc reagents in terms of enantioselectivity (up to >99 % ee). More importantly, the chirality matching between different chiral sources, C₂‐axial binaphthol and sp³‐central chiral phosphine, was crucial to the enantioselective induction in this reaction. The experimental results indicated that our chiral ligand (R,S,S)‐ L1 ‐ and (R,S)‐ L4 ‐based bimetallic complex catalyst system exhibited the highest catalytic performance to date in terms of enantioselectivity and conversion even in the presence of 0.005 mol % of catalyst (S/C=20 000, turnover number (TON)=17 600). We also studied the tandem silylation or acylation of enantiomerically enriched zinc enolates that formed in situ from copper‐ L4 ‐complex‐catalyzed conjugate addition, which resulted in the high‐yield synthesis of chiral silyl enol ethers and enoacetates, respectively. Furthermore, the specialized structure of the present multifunctional N,O,P ligand L1 or L4 , and the corresponding mechanistic study of the copper catalyst system were investigated by ³¹P NMR spectroscopy, circular dichroism (CD), and UV/Vis absorption.     

Coumarin-based urea-amide scaffold in ratiometric fluorescence sensing of CN−

Coumarin-based urea and urea–amide scaffolds 1–3 have been designed and synthesized for the selective and naked eye detection of cyanide ion. Of the three, compound 3 exhibits ratiometric fluorescence change selectively in the presence of CN^? and validates the rationality in designing anion receptor. Upon interaction with CN^?, the color of the solution of 3 in CH₃CN under UV exposure becomes bright yellow, which is beneficial for its naked eye detection. Addition of CN^? of ～10^?4 M brings nice color change from colourless to yellow in ordinary light. The sensing event is supposed to be due to nucleophilic addition of CN^? to the coumarin unit enabling intramolecular charge transfer (ICT) mechanism.     

Identification of source terms in wave equation with dynamic boundary conditions

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fréchet differentiability of the Tikhonov functional is studied, and a gradient formula is obtained via the solution of an associated adjoint problem. Then, the Lipschitz continuity of the gradient is proved. Furthermore, the existence and the uniqueness for the minimization problem are discussed. Finally, some numerical experiments for the reconstruction of an internal wave force are implemented via a conjugate gradient algorithm.     

Higher-Order $(F,\alpha, \beta, \rho, d, E) $-Convexity in Fractional Programming

In this paper we define higher order $(F,\alpha, \beta, \rho,d, E)$-convex function with respect to $E$-differentiable function $K$ and obtain optimality conditions for nonlinear programming problem (NP) from the concept of higher order $(F,\alpha, \beta, \rho,d)$-convexity. Here, we establish Mond-Weir and Wolfe duality for (NP) and utilize these duality in nonlinear fractional programming problem.     

Generalized local duality,canonical modules,and prescribed bound on projective dimension

We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality theorem which extends, to a much broader class of rings, previous results by Herzog-Zamani and Suzuki. As an application, we establish a prescribed upper bound for the projective dimension of a module satisfying suitable cohomological conditions, and we derive some freeness criteria and questions of Auslander-Reiten type. Along the way, we prove a new characterization of Cohen-Macaulay modules which truly relies on generalized local cohomology, and in addition we introduce and study a generalization of the notion of canonical module.