Second-order conditions in c1, 1 optimization with applications

Second-order necessary conditions for inequality and equality constrained C^{1, 1} optimization problems are derived. A constraint qualification condition which uses the recent generalized second-order directional derivative is employed to obtain these conditions. Various second-order sufficient conditions are given under appropriate conditions on the generalized second-order directional derivative in a neighborhood of a given point. An application of the secondorder conditions to a new class of nonsmooth C^{1, 1} optimization problems with infinitely many constraints is presented.     

Optimality Conditions for Nonconvex Constrained Optimization Problems

Abstract

We present optimality conditions for a class of nonsmooth and nonconvex constrained optimization problems. To achieve this aim, various well-known constraint qualifications are extended based on the concept of tangential subdifferential and the relations between them are investigated. Moreover, local and global necessary and sufficient optimality conditions are derived in the absence of convexity of the feasible set. In addition to the theoretical results, several examples are provided to illustrate the advantage of our outcomes.     

Integrated scheduling of crane handling and truck transportation in a maritime container terminal

This paper studies the interactions between crane handling and truck transportation in a maritime container terminal by addressing them simultaneously. Yard trucks are shared among different ships, which helps to reduce empty truck trips in the terminal area. The problem is formulated as a constraint programming model and a three-stage algorithm is developed. At the first stage, crane schedules are generated by a heuristic method. At the second stage, the multiple-truck routing problem is solved based on the precedence relations of the transportation tasks derived from the first stage. At the last stage a complete solution is constructed by using a disjunctive graph. The three procedures are linked by an iterative structure, which facilitates the search for a good solution. The computational results indicate that the three-stage algorithm is effective for finding high-quality solutions and can efficiently solve large problems.     

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.     

成教实验教学与技能竞赛对接模式的探索

针对成教生生源结构和学习特点,以分析化学实验教学为例,在日常教学中通过强化学生实验操作培训,提高学生分析检测能力。藉举办化学分析工技能竞赛,促进教师教学形式的转变,提升学生自主探究能力。将实验教学与技能竞赛相对接,增强学生就业竞争力,提升学院办学影响力与认可度。     

Characterization of Standard Reference Material 2941, uranyl-ion-doped glass, spectral correction standard for fluorescence

Standard Reference Material^® (SRM^®) 2941 is a cuvette-shaped, uranyl-ion-doped glass, recommended for use for relative spectral correction of emission and day-to-day performance validation of fluorescence spectrometers. Properties of this standard that influence its effective use or contribute to the uncertainty in its certified emission spectrum have been explored here. These properties include its photostability, absorbance, dissolution rate in water, anisotropy, temperature coefficient of fluorescence intensity, and fluorescence lifetimes. The expanded uncertainties in the certified spectrum are about 4% around the peak maximum at 526 nm, using an excitation wavelength of 427 nm. The SRM also exhibits a strong resistance to photodegradation, with no measurable decrease in fluorescence intensity even after 8 h of laser irradiation.     

Ground states of two-component attractive Bose–Einstein condensates I: Existence and uniqueness

We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in ${\mathbb{R}}^2$, where the intraspecies interaction $(?a_1,?a_2)$ and the interspecies interaction ?β are both attractive, $i.e$, $a_1$, $a_2$ and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated $L^2$-critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as $\beta \nearrow {\beta }^{?}=a^{?}+\sqrt{(a^{?}?a_1)(a^{?}?a_2)}$, where $0<a_i<a^{?}:={6w6}_2^2$ ($i=1,2$) is fixed and w is the unique positive solution of $\mathrm{\Delta }w?w+w^3=0$ in ${\mathbb{R}}^2$. The semi-trivial limit behavior of ground states is tackled in the companion paper [12].     

Optical analysis of polymer powder materials for Selective Laser Sintering

This study increases the basic understanding of optical material properties of polymer powders used in selective laser sintering (SLS). Therefore, different polymer powder materials were analyzed regarding their optical material properties with an integration spheres measurement setup. By the measurements a direct connection between the absorption behavior of the solid material and the overall optical material characteristics of the same material in powdery form could be shown. The results were used to develop an advanced explanation model for the optical material properties of powders. At present, existing explanation models only consider the occurring of multiple reflections in the gaps between the particles to explain the overall optical material properties of powder materials. Thus, by also considering the absorption behavior of the single particles, the basic understanding of the beam-matter interaction and their effect on the optical material properties of powder materials can be expanded.     

Modeling the solid-like behavior of entangled polymer nanocomposites at low frequency regimes

A theory for the linear viscoelastic behavior of entangled polymeric liquids reinforced with non-aggregated colloidal nanoparticles is presented. Composites with low filler concentration and strong polymer-particle interaction are considered. A fraction of entangled chains is assumed to be reversibly adsorbed on the surface of fillers, due to the affinity between the polymer molecules in the matrix and dispersed filler particles. The relaxation of the system is analyzed by the combination of stress relaxation functions for free and adsorbed polymer chains. It is demonstrated that the emergence of solid-like behavior at low frequency regimes, is due to the significant slow down in relaxation of adsorbed chains. Fitting the model predictions with relevant experimental data indicates that while the effect of constraint release should be considered to obtain a reasonable estimation of neat polymer behavior, the linear combination of stress relaxation functions of free and adsorbed chains (i.e., no thermal constraint release) leads to a better agreement with experimental data of filled systems.     

Optimality conditions for nonsmooth mathematical programs with equilibrium constraints,using convexificators

In this paper, we deal with constraint qualifications, stationary concepts and optimality conditions for a nonsmooth mathematical program with equilibrium constraints (MPEC). The main tool in our study is the notion of convexificator. Using this notion, standard and MPEC Abadie and several other constraint qualifications are proposed and a comparison between them is presented. We also define nonsmooth stationary conditions based on the convexificators. In particular, we show that GS-stationary is the first-order optimality condition under generalized standard Abadie constraint qualification. Finally, sufficient conditions for global or local optimality are derived under some MPEC generalized convexity assumptions.