关于向量极值问题的研究

在局部凸实拓扑向量空间中,给出了广义锥类凸向量映射的概念,研究了目标函数和约束函数均为广义锥类凸映射的向量极值问题．首先,用拟切锥给出了向量极值问题极小点的充分条件;其次,用拟切锥给出了向量极值问题对应的标量化问题极小点的充分条件;最后,定义了极值问题的Lagrangian函数,给出了Lagrangian函数鞍点的概念,用拟切锥获得了鞍点的充分条件．     

Hilbert空间上非凸规划的Kuhn-Tucker鞍点定理

本文主要讨论了Hilbert空间上带不等式约束的非凸规划的解与Lagrange式鞍点之间的关系.利用闭包函数作为工具,在此条件,存在(x_0,μ_0)conv(epif))且在x_0∈domf条件下,证明了Lagrange式存在鞍点是该非凸规划有解的必要条件.     

集函数多目标规划的最优性充分条件

在较弱凸性条件下,研究了一类可微n-集函数多目标规划问题的可行解是弱有效解的最优性充分条件.首先,对已知集X的子集的@-代数A的n-折积An,定义了伪度量d(R,S),并给出了n-折积An的子集S的特征函数<h,Is>;其次,通过特征函数给出了集函数在子集So上可微的定义及集函数在子集So上关于第i个变量Si的偏导数定义;再次,给出了多目标规划问题(VP)的弱有效解的概念;最后,分别在目标函数和约束函数3种较弱凸性条件下,给出了集函数多目标规划问题的可行解是弱有效解的3个最优性充分条件.     

一类非光滑连续时间的多目标优化问题

讨论了一类非光滑连续时间非线性多目标优化问题在函数广义凸性假设下的最优性充分条件和必要条件     

乘积空间中的极小化问题

本文利用Banach空间中的隐函数定理,对乘积空间等式约束问题建立了最优性的一阶必要条件(?)同时,对不等式约束问题讨论了Lagrange乘子的存在性以及最优解与鞍点的关系.     

广义F—不变凸多目标规划的对偶性

研究了Ｂａｎａｃｈ空间中含广义Ｆ－不变凸函数的多目标规划问题的对偶性。介绍了约束规格及引理１，讨论了这类多目标规划问题的ｗｏｌｆｅ型对偶和Ｍｏｎｄ－Ｗｅｉｒ型对偶，并在较弱Ｆ－不变凸的假设下获得了强对偶、弱对偶和其它一些对偶结果。     

Filter方法在不等式约束优化问题中的应用

用filter方法取代罚函数进行线性搜索,又利用序列线性方程组获得搜索方向,使得迭代点能够保证目标函数或约束函数充分下降,在一定假设条件下可以收敛到原问题的最优解。     

非光滑优化问题的最优性条件和对偶

在函数广义凸意义下 ,获得了非光滑非线性优化问题的最优性必要条件和充分条件 ,建立了问题的对偶模型并得到对偶结果 .     

半无穷维广义F不变凸多目标规划的最优性条件

研究了Ｂａｎａｃｈ空间中广义Ｆ不变凸多目标规划问题的最优性条件，获得了可行解是有效解或弱有效解的ＫｕｈｎＴｕｃｋｅｒ型最优性充分条件和必要条件．     

波导环境多目标时延-多普勒解卷成像

有源声呐感兴趣的参量是目标距离和径向速度,它们无法直接观测得到,需要通过估计而获得。利用波导多路径环境多目标时延-多普勒模型,可以导出采样互模糊度函数均值是发射信号自模糊度函数与广义目标反射性密度函数的两维卷积,其中广义目标反射性密度函数为信道扩展函数与目标反射性密度函数的两维卷积。依据信息理论最小Csiszar鉴别准则,可导出R-L(Richardson-Lucy)迭代解卷算法,对采样互模糊度函数均值进行两维迭代解卷积,消除发射信号和信道引入的模糊,序贯地实现时延-多普勒两维像的估计,进而获得多目标的时延和多普勒参量估计。仿真结果和海上实验数据分析验证了R-L解卷算法的可行性和有效性,较之常规的匹配滤波和维纳滤波算法,R-L算法有效地提高了时延和多普勒估计的分辨力和精度。     

向量变分不等式的标量局部唯一解

首先 讨论了向量变分不等式同向量最优化问题解之间的关系，然后证明了向量变分不等式解的Ｋ－Ｔ必要和充分条件，最后引入标量局部唯一解的概念，在适当条件下，证明了向量变分不等式存在标量局部唯一解。     

广义向量最优化问题的Mond—Weir型对偶

对广义向量最优化问题建立了Ｍｏｎｄ－Ｗｅｉｒ型对偶，证明了原问题和对偶问题之间的弱对偶定理、直接对偶定量和逆对偶定理。     

Analysis of nonlinear channel friction inverse problem

Based on the Backus-Gilbert inverse theory, the singular value decomposition (SVD) for general inverse matrices and the optimization algorithm are used to solve the channel friction inverse problem. The resolution and covariance friction inverse model in matrix form is developed to examine the reliability of solutions. Theoretical analyses demonstrate that the convergence rate of the general Newton optimization algorithm is in the second-order. The Wiggins method is also incorporated into the algorithm. Using the method, noise can be suppressed effectively, and the results are close to accurate solutions with proper control parameters. Also, the numerical stability can be improved. Translated from Journal of Zhejiang University (Engineering Science), 2005, 39(10): 1 603–1 608 [译自: 浙江大学学报(工学版)]     

Multicriteria optimization of cold-formed thin-walled beams with generalized open shape under different loads

The paper presents an analysis of the optimal design of cold-formed beams with generalized open shapes under pure bending, uniformly distributed loads, concentrated loads and axial loads with constant bending moment. The optimization problem includes the cross section area as the first objective function and the deflection of a beam as the second one. The geometric parameters of cross sections are selected as design variables. The set of constraints includes global stability condition, selected forms of local stability conditions, strength condition and technological and constructional requirements in a form of geometric relations. The strength and stability conditions are formulated and analytically solved using mathematical equations. The optimization problem is formulated and solved with help of the Pareto concept of optimality. The numerical procedure, based on the Messac normalized constraint method, include discrete, continuous and discrete-continuous sets of design variables. Results of the numerical analysis for different loads of beams with monosymmetrical cross section shapes are presented in tables.     

Effective shaping of cold-formed thin-walled channel beams with double-box flanges in pure bending

The paper is devoted to cold-formed thin-walled channel beams with double-box flanges. Geometric properties of the C-section are described in terms of dimensionless parameters. The warping function and the warping inertia moment are analytically determined. The optimization criterion and the dimensionless objective functions are defined as a quality measure. The space of feasible solutions is constrained by the strength, global, local buckling, and geometric conditions. Analytical solutions of the problems of global and local buckling for thin-walled beams are presented. Results of the numerical calculations of the optimal shaping problem are presented in tables and figures.     

The convexity about ultimate bearing hypersurfaces of structures

The relationship between the convexity on the ultimate bearing surface of a structure and the secondorder effects of loads is discussed. All of generalized non-overload forces acted on a structure forms a convex set when ignoring the second-order effects (coupling effects between the generalized forces). It is true also when the Hessian matrix composed of the second-order partial derivatives on the hypersurface about the ultimate bearing of the structure is negative definite. The outward convexity is kept when the surface is expressed by certain dimensionless parameters. A series of properties based on the convexity are pointed out. Some applications in the analysis of bearing capacity of structures were illustrated with examples. The study shows that an evaluation about the bearing capacity state of a complex structure can be made on the basis of several points on the surface of the ultimate bearing of the structure.