On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

正交设计-紫外分光光度法测定青蒿中的青蒿素

以干青蒿叶为原料,考察石油醚萃取青蒿素的工艺条件,如温度、时间、溶剂量及超声功率等因素,正交法确定了最佳萃取工艺条件为温度40℃,超声功率90W,时间20min（两次）,液固比120∶1（mL.g-1）。紫外分光光度法直接测定不同产地青蒿中青蒿素的含量,结果表明：用超声波强化石油醚萃取青蒿素与常规浸泡法石油醚萃取比较,用超声波可以大大缩短萃取时间,提高了萃取率。     

电流引线迫流冷却传热分析

如何降低电流引线向低温环境的漏热,是超导电力技术领域的一项重要课题.文中概述了电流引线研究进展,建立了电流引线迫流冷却传热模型,并分析了氮气迫流冷却作用,推导了电流引线温度分布和最优长度-横截面积比(ORLA)函数式.自然蒸发迫流冷却对最优长度-横截面积比(ORLA)影响较小.     

高场超导MRI系统铁磁屏蔽的几何优化

磁共振成像（MRI）系统是一种重要的医学影像诊断设备,它根据核磁共振原理对处于静磁场中的人体器官进行成像,具有清晰度高和任意层面成像等优点,在医学检查和诊断方面有着重要的作用,与低场MRI相比,高场MRI系统可提高质子的磁化率,增加图像的信噪比,缩短MRI信号采集时间,从而使脑功能成像的信号变化更为明显;但是较高的背景...     

On a constructive approach to optimality conditions for convex SIP problems with polyhedral index sets

In the paper, we consider a problem of convex Semi-Infinite Programming with an infinite index set in the form of a convex polyhedron. In study of this problem, we apply the approach suggested in our recent paper [Kostyukova OI, Tchemisova TV. Sufficient optimality conditions for convex Semi Infinite Programming. Optim. Methods Softw. 2010;25:279–297], and based on the notions of immobile indices and their immobility orders. The main result of the paper consists in explicit optimality conditions that do not use constraint qualifications and have the form of criterion. The comparison of the new optimality conditions with other known results is provided.     

Novel design model for the stator currents subsystem of induction motors

The stator currents subsystem is a vital element of many high-performance induction motor control schemes. While there are several control techniques available for this subsystem, traditional linear controllers are still widely used because of its simplicity and proven effectiveness. However, the traditional simplified design-model lacks important information, necessary for the design of high-performance and robust controllers. In this article a novel design-model intended for linear controller formulation and evaluation is developed. This new mathematical representation captures several elements which are missing in the traditional representation, maintaining at the same time a similar level of simplicity. Along the derivation of this new representation several models of decreasing complexity and comprehensiveness are also presented together with a critical classification. This classification is intended to aid the designer in choosing the appropriate mathematical representation for specific purposes. Finally, the article is accompanied with experimental findings which illustrate the use of the proposed model.     

Statistical testing of optimality conditions in multiresponse simulation-based optimization

This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.     

A CONSTRAINT QUALIFICATION FOR CONVEX PROGRAMMING

1. IntroductionLet X be the n-dimensional Euclidean space Rad. Denote the transpose of the columnvector y by yT. Suppose that R7 and nit R= are the n-dimensional vector sets with nonnegative and positive components, whose elements are denoted by y 3 0 and y > 0, respectively.Write R for the nonnegative real number set.Consider a nondiffereatiable convex programming problem:We assume that f(x), gi(x),..', g.(x) are finite reaLvalued continuous, convex functions on X, but not necessarily d…