SUPER EFFICIENCY IN THE NEARLY CONE-SUBCONVEXLIKE VECTOR OPTIMIZATION WITH SET-VALUED FUNCTIONS

Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikeness, some characterizations of the super efficiency are given in terms of scalarization and Lagrangian multipliers. Related results are generalized.

BENSON PROPER EFFICIENCY IN THE NEARLY CONE-SUBCONVEXLIKE VECTOR OPTIMIZATION WITH SET-VALUED FUNCTIONS

Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.

SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES

We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points,related to the so-called Rolewicz’s property(α).We give a characterization of those points in terms of continuity properties of the identity mapping.The connection between these two geometric properties is established,and finally an application to approximative compactness is given.

MARTINGALE REPRESENTATION IN NEARLY UNIFORMLY CONVEX SPACES

In this paper we give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by Landers and Rogge.

Checking weak and strong optimality of the solution to interval convex quadratic program

In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.

APPROXIMATING COMMON FIXED POINTS OF NEARLY ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings. We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.

DOUBLE INERTIAL PROXIMAL GRADIENT ALGORITHMS FOR CONVEX OPTIMIZATION PROBLEMS AND APPLICATIONS

In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.

Higher-Order Minimizers and Generalized (F,<i>ρ</i>)-Convexity in Nonsmooth Vector Optimization over Cones

In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

CFG桩在城市临铁软弱土层地基处理中的优势探讨

结合具体工程实例,通过施工方案比选,讨论了CFG桩在处理城市临铁软弱土层地基中的优势,就CFG桩施工技术要点展开了详细的研究,并提出了施工质量控制措施。考虑到城市临铁软弱土层地基的复杂性,研究进行了复合地基静荷载试验。结果表明,CFG桩可以有效提高地基承载力,在软弱土层地基处理中具有重要应用价值。

邻近水库软弱围岩小净距隧道开挖方案优化研究

以义东高速公路防军隧道为依托,对邻近水库软弱围岩小净距隧道开挖方案进行优化比选。运用有限元软件Midas·GTS·NX建立开挖方案优化前后2种方案的隧道模型,结合数值模拟结果和现场监测数据对隧道围岩应力、位移和塑性区分布进行分析对比。研究结果表明:从力学角度出发,2种方案对围岩稳定性的控制效果相差不大。围岩条件较好时,留核心土法开挖对保证施工安全、降低施工成本、缩短工期均能起到较好效果。综合考虑施工地质条件及工法特点,采用变更后的留核心土法更加符合工程实际。

Weak Convergence Theorems for Nonself Mappings

Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {kn^（i）} [1, ∞） （i = 1, 2）, and F ：= F（T1）∩ F（T2） ≠ 0. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Frechet differentiable norm or its dual E^＊ has Kadec-Klee property, then weak convergence theorems are obtained.

GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.

A Weak Convergence Theorem for A Finite Family of Asymptotically Nonexpansive Mappings

The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.

Coincidence Points and Almost-like Coincidence Points on Generalized ConvexSpaces with Applications

We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.

THE EXISTENCE THEOREM OF THE CONE-WEAK SUBDIFFERENTIAL OF SET-VALUED MAPPING

In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.

不确定多目标优化问题鲁棒ε-拟弱有效解的最优性和对偶性

研究了一类具有不确定因素的多目标优化问题.首先,在广义凸性条件下,给出了多目标优化问题鲁棒ε-拟弱有效解的最优性充分条件.其次,给出了相应的Mond-Weir型和Wolfe型对偶模型,并分别讨论了原问题与两类对偶问题之间的对偶关系,得到了相应的弱对偶、强对偶以及逆对偶结论.

Near Convexity, Near Smoothness and Approximative Compactness of Half Spaces in Banach Spaces

The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characteriza- tions such that every half-space in Banach space X and every weak^＊ half-space in the dual space X^＊ are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.

河套盆地巨厚弱成岩覆盖区地震勘探成像技术应用研究

河套盆地由于快速堆积、欠压实作用等原因,4000~5000m以上均为弱成岩覆盖,地震资料成像精度受到严重影响。针对巨厚弱成岩引起的勘探难题,开展了基于目的层响应特征的可控震源激发信号设计、基于多信息约束的精细近地表建模及全深度Q值补偿、基于大地坐标的近地表类型分区去噪、基于平面属性的断层解释等技术的应用,资料品质得到了提升。通过相关技术的应用,主要目的层频带拓宽了10Hz左右,断面清楚,断点清晰干脆,能够满足地震解释需求,探明了吉兰泰和巴彦两个油田。通过针对性的采集、处理、解释一体化技术的研究,解决了该区域地震波吸收衰减严重、资料信噪比低、复杂构造区成像精度差、储层难以预测等关键难题,可以指导类似地区的勘探施工。

近等基因系法对小麦显性矮源的研究

【目的】开拓小麦育种新矮源,克服自小麦矮化育种“绿色革命”以来,仅使用Rht1、Rht2、Rht8等少数几个隐性矮源的局限性,为选育高度集约化的小麦新品种提供条件。【方法】将国内外已定名的5个显性矮源Rht10、Rht3、Rht12、Rht21、奥尔森矮(Olesen dwarf)和西南大学农学与生物科技学院培育与征集的7个致矮力弱的显性矮源回交导入4个中、高秆(85～105cm)轮回父本品种(BC4F1),建立了4套矮秆基因的近等基因系。2005～2006两年,在非竞争群体条件下开展了近等基因系的多因素品系比较试验,研究矮源及轮回父本遗传背景两个主因素对近等基因系主要农艺性状的影响效应。【结果】12个显性矮源在本试验统一遗传背景条件下株高为37.9～74.3cm,显性矮源的株高与其株粒重呈高度正相关(r=0.8884),株高每上升1cm,则株粒重增加0.24g。随显性矮源株高的提升、致矮力减弱,其近等基因系的农艺性状得到改善。显性矮源的株高提升到60cm以上时,即有可能达到和超过中、高秆轮回父本的单株生产力,从而作为新型矮源应用于小麦矮化育种。此外,12个显性矮源具有一致的延迟早熟轮回父本抽穗以及降低轮回父本千粒重的多效性效应,这些不利的多效性效应可以通过轮回父本遗传背景的修饰作用加以改良。【结论】株高在50cm以下的强致矮力显性矮源,难以直接用于小麦育种,但通过矮秆主基因突变以及特殊遗传背景的修饰等途径可以衍生出株高呈不同程度提升、以致达到70～80cm理想株高的弱致矮力显性矮源。加强株高提升的弱致矮力显性矮源的研究是将显性矮源应用于小麦杂交育种的有效途径。推荐株高在60～75cm的弱致矮力显性矮源SW07、SW05、女水妖矮、SW02、Rht21用于小麦矮化育种。