Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

含参广义集值强向量平衡问题的稳定性

本文借助集合极限的性质和弱f-性假设证明了含参广义集值强向量平衡问题解集映射的下半连续性,其方法不同于最近文献(Zhao,2016和Meng,2018).此外,建立了含参广义集值强向量平衡问题解集连通性的充分条件,并举例验证了所得结果的正确性.本文得结果推广和改进了已有文献(Gong,2008,Xu,2009,Chen,2010,Xu,2013和Zhao,2013)中相应结果.     

Recrystallization processes in snte thin films implanted with the nobel gas ions (Kr,Xe)

Abstract

The results of investigation of the quasi-Cherenkov (parametric) X-ray emission of 4.5 GeV electrons in diamond and quartz crystals are presented. A noticeable increase in X-ray photons yield has been observed under the influence of external factors (acoustic waves, temperature gradient).     

飞秒时间分辨荧光非共线光参量放大光谱技术

时间分辨荧光光谱技术是研究激发态弛豫、能量传递以及电荷转移等光化学过程的重要且直接的工具．飞秒时间分辨荧光非共线光参量放大光谱技术是一种新发展的具有高时间分辨率、宽探测带宽、高增益的时间分辨光谱技术．本文对该技术的基本原理与工作特性、系统配置、荧光收集和会聚、数据采集模式、时问分辨光谱数据处理等进行了系统阐述．最后简单介绍了飞秒时间分辨荧光非共线光参量放大光谱技术在物理、生物和化学领域的3个典型应用,并以此展现该技术的高时间分辨率、宽光谱探测及高增益优势．     

Trace gas detection of benzene,toluene, p-, m- and o-xylene with a compact measurement system using cantilever enhanced photoacoustic spectroscopy and optical parametric oscillator

A compact measurement system based on a novel combination of cantilever enhanced photoacoustic spectroscopy (CEPAS) and optical parametric oscillator (OPO) was applied to the gas phase measurement of benzene, toluene, and o-, m- and p-xylene (BTX) traces. The OPO had a band width (FWHM) of 1.3 nm, was tuned from 3237 to 3296 nm in steps of 0.1 nm and so spectra of BTX at different concentrations were recorded. The power emitted by the OPO increased from 88 mW at 3237 nm to 103 mW at 3296 nm. The univariate detection limits (3σ, 0.951 s) for benzene, toluene, p-, m- and o-xylene at 3288 nm were 12.0, 9.8, 13.2, 10.1 and 16.0 ppb, respectively. Multivariate data analysis using science-based calibration was used to resolve the interference of the analytes. The multivariate detection limits (3σ, 3237–3296 nm, 591 spectral points each 0.951 s) for benzene, toluene, p-, m- and o-xylene in the multi-compound sample, where all other analytes and water interfere were 4.3, 7.4, 11.0, 12.5 and 6.2 ppb, respectively. Without interferents, the multivariate detection limits varied between 0.5 and 0.6 ppb. The sum of the cross-selectivities (3237–3296 nm, 591 spectral points, each 0.951 s) per analyte were below 0.05 ppb/ppb, with an average of 0.038 ppb/ppb. The cross-selectivity of water to the analytes was on average 1.22 × 10⁻⁴ ppb/ppb. The OPO is small in size (L × W × H 125 × 70 × 45 mm), commercially available, and easy to operate and integrate to setups. The combination with sensitive CEPAS enables compact measurement systems for industrial as well as environmental trace gas monitoring.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Fiber optical parametric amplifiers in optical communication systems

The prospects for using fiber optical parametric amplifiers (OPAs) in optical communication systems are reviewed. Phase‐insensitive amplifiers (PIAs) and phase‐sensitive amplifiers (PSAs) are considered. Low‐penalty amplification at/or near 1 Tb/s has been achieved, for both wavelength‐ and time‐division multiplexed formats. High‐quality mid‐span spectral inversion has been demonstrated at 0.64 Tb/s, avoiding electronic dispersion compensation. All‐optical amplitude regeneration of amplitude‐modulated signals has been performed, while PSAs have been used to demonstrate phase regeneration of phase‐modulated signals. A PSA with 1.1‐dB noise figure has been demonstrated, and preliminary wavelength‐division multiplexing experiments have been performed with PSAs. 512 Gb/s have been transmitted over 6,000 km by periodic phase conjugation. Simulations indicate that PIAs could reach data rate x reach products in excess of 14,000 Tb/s × km in realistic wavelength‐division multiplexed long‐haul networks. Technical challenges remaining to be addressed in order for fiber OPAs to become useful for long‐haul communication networks are discussed.

     

Trends in ultrashort and ultrahigh power laser pulses based on optical parametric chirped pulse amplification

Since the proof-of-principle demonstration of optical parametric amplification to efficiently amplify chirped laser pulses in 1992,optical parametric chirped pulse amplification(OPCPA)became the most promising method for the amplification of broadband optical pulses.In the meantime,we are witnessing an exciting progress in the development of powerful and ultrashort pulse laser systems that employ chirped pulse parametric amplifiers.The output power and pulse duration of these systems have ranged from a few gigawatts to hundreds of terawatts with a potential of tens of petawatts power level.Meanwhile,the output pulse duration based on optical parametric amplification has entered the range of fewoptical-cycle field.In this paper,we overview the basic principles,trends in development,and current state of the ultrashort and laser systems based on OPCPA,respectively.