The Lagrangian Globalization Method for Nonsmooth Constrained Equations

The difficulty suffered in optimization-based algorithms for the solution of nonlinear equations lies in that the traditional methods for solving the optimization problem have been mainly concerned with finding a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. One method to overcome this difficulty is the Lagrangian globalization (LG for simplicity) method. This paper extends the LG method to nonsmooth equations with bound constraints. The absolute system of equations is introduced. A so-called Projected Generalized-Gradient Direction (PGGD) is constructed and proved to be a descent direction of the reformulated nonsmooth optimization problem. This projected approach keeps the feasibility of the iterates. The convergence of the new algorithm is established by specializing the PGGD. Numerical tests are given. This author's work was done when she was visiting The Hong Kong Polytechnic University. His work is also supported by the Research Grant Council of Hong Kong.     

Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities

In this paper, we present a smoothing Newton-like method for solving non-linear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.     

Development of a solid‐phase microextraction fiber by the chemical binding of graphene oxide on a silver‐coated stainless‐steel wire with an ionic liquid as the crosslinking agent

Graphene oxide was bonded onto a silver‐coated stainless‐steel wire using an ionic liquid as the crosslinking agent by a layer‐by‐layer strategy. The novel solid‐phase microextraction fiber was characterized by scanning electron microscopy, energy‐dispersive X‐ray spectroscopy and Raman microscopy. A multilayer graphene oxide layer was closely coated onto the supporting substrate. The thickness of the coating was about 4 μm. Coupled with gas chromatography, the fiber was evaluated using five polycyclic aromatic hydrocarbons (fluorene, anthracene, fluoranthene, 1,2‐benzophenanthrene, and benzo(a)pyrene) as model analytes in direct‐immersion mode. The main conditions (extraction time, extraction temperature, ionic strength, and desorption time) were optimized by a factor‐by‐factor optimization. The as‐established method exhibited a wide linearity range (0.5–200 μg/L) and low limits of determination (0.05–0.10 μg/L). It was applied to analyze environmental water samples of rain and river water. Three kinds of the model analytes were quantified and the recoveries of samples spiked at 10 μg/L were in the range of 92.3–120 and 93.8–115%, respectively. The obtained results indicated the fiber was efficient for solid‐phase microextraction analysis.     

Preparation and characterization of a polystyrene/bovine serum albumin nanoparticle‐coated capillary for chiral separation using open‐tubular capillary electrochromatography

Polystyrene (PS) nanoparticles coated by BSA, hereafter denoted as PS/BSA, were prepared and chemically immobilized for the first time onto a capillary inner wall for open‐tubular CEC (OTCEC). EOF and scanning electron micrography were used to characterize the prepared nanoparticle‐coated capillaries. To investigate the performance of the prepared columns in OTCEC, chiral separation of d ,l ‐tryptophan (dl ‐Trp) was performed in monolayer BSA‐modified capillary and PS/BSA nanoparticle‐coated columns. The results indicated that the nanoparticle‐modified column afforded a higher resolution compared with the monolayer type. Rapid enantioseparation of dl ‐Trp (within 3 min) was achieved with the PS/BSA‐immobilized column using an electroosmotic pump‐assisted CEC. Enantiomer separations of other compounds like dl ‐tyrosine and warfarin were also achieved with the column. Besides, run‐to‐run and column‐to‐column repeatabilities of the PS/BSA‐coated column in the chiral separation were systematically introduced.     

解非线性约束方程的拉格朗日全局投影方法

基于最优化方法求解约束非线性方程组的一个突出困难是计算 得到的仅是该优化问题的稳定点或局部极小点,而非方程组的解点.由此引出的问题是如何从一个稳定点出发得到一个相对于方程组解更好的点. 该文采用投影型算法,推广了Nazareth-Qi$^{[8,9]}$ 求解无约束非线性方程组的拉格朗日全局算法(Lagrangian Global-LG)于约束方程上; 理论上证明了从优化问题的稳定点出发,投影LG方法可寻找到一个更好的点. 数值试验证明了LG方法的有效性.     

等式与界约束非线性优化信赖域算法的全局收敛

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ :ｍｉｎｉｍｉｚｅｆ(ｘ)ｓｕｂｊｅｃｔｔｏＣ(ｘ) =0 ,　ａ≤ｘ≤ｂ ,( 1 .1 )ｗｈｅｒｅｆ(ｘ) :Ｒｎ→Ｒ ,Ｃ(ｘ) =(ｃ1(ｘ) ,ｃ2 (ｘ) ,...,ｃｍ(ｘ) ) Ｔ:Ｒｎ→Ｒｍ ａｒｅｔｗｉｃｅｃｏｎｔｉｎｕｏｕｓｌｙｄｉｆｆｅｒｅｎｔｉａｂｌｅ,ｍ≤ｎ ,ａ ,ｂ∈Ｒｎ.Ｔｒｕｓｔｒｅｇｉｏｎａｌｇｏｒｉｔｈｍｓａｒｅｖｅｒｙｅｆｆｅｃｔｉｖｅｆｏｒｓｏｌｖｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉ…     

基于ip-iq理论的改进谐波检测方法

有源电力滤波器(APF)是电力系统中实现电能质量管理的关键设备,谐波检测作为APF的关键技术之一,检测的精度和响应速度直接决定了APF的整体性能。介绍了传统的基于瞬时无功功率理论的ip-iq谐波电流检测算法; 针对其检测精度受锁相环输出相位误差影响,以及低通滤波器的存在限制了谐波检测系统的响应速度,提出了应用锁频环技术,产生与电网电压同频的单位正余弦信号的一种改进谐波检测算法; 并提出采用滑动平均滤波器(MAF)代替低通滤波器提高其响应速度以及改善谐波检测精度; 对改进的检测算法进行了理论分析,通过MATLAB进行仿真研究,理论分析和仿真结果都证明了该方法的有效性。     

GLOBAL CONVERGENCE OF NONMONOTONIC TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION

§ 1　 IntroductionIn this paper we study the following nonlinear equality constrained optimization prob-lem:minimize f(x) ,subjectto h(x) =0 ,(P)where h(x) =(h1 (x) ,h2 (x) ,...,hm(x) ) T,f and hi(i=1 ,2 ,...,m) are Rn→R twice conti-nously differentiable(m≤n) .Many authors have studied the problem(P) with trustregion method(see,references[1～ 3 ] ) .These methods have the same property:to enforce strict monotonicity for meritfunction at every iteration.Paper[4 ] shows thatstrictmonotonic …