An abstract symmetric framework for duality in mathematical programming

The paper offers an abstract structure called environment (of mathematical programming) in which a pair of dual programs is settled symmetrically. Given an environment, the concepts of an optimization program, its dual and the associated Lagrangean are formalized and studied. The usual asymmetries in certain types of mathematical programming are due to selection of asymmetric environments. Common types of programming like: linear, nonlinear, convex, integer etc. are reviewed in the proposed framework.     

英国国家科研与创新署学科交叉研究资助机制及启示

Newly established in 2018, the UK Research and Innovation (UKRI) strengthens the strategic coordination of the UK research and innovation system by bringing together seven Research Councils, Research England, and Innovate UK. Through its nine organizations, UKRI funds multidisciplinary and interdisciplinary research in a number of priority areas. It also runs the Strategic Priorities Fund to support multidisciplinary and interdisciplinary research in strategic areas identified by government policies as well as the Global Challenges Research Fund to promote challenge-led interdisciplinary research needed by developing countries. The UKRI makes significant efforts to engage stakeholders in the development, design, and implementation of multidisciplinary and interdisciplinary programs. It has also developed a range of mechanisms to improve the evaluation of multidisciplinary and interdisciplinary projects. Chinese science and innovation funding agencies could draw upon the UKRI experience from four aspects to advance interdisciplinary research in China.     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

粉末衍射峰形拟合程序包CPOWDER

开发了一个Ｘ射线和中子粉末衍射峰形拟合程序包ＣＰＯＷＤＥＲ，它是由多个最小二乘峰形拟合程序与蒙特卡罗分峰程序组成的。最小二乘峰形拟合程序可用于约束条件下的峰形拟合分析，蒙特卡罗分峰程序可用于寻找全局最优解，为最小二乘拟合程序提供优质的峰形参数初始值，两者结合使用特别适合于多个严重重叠峰的分离。     

Finding dominators via disjoint set union

The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-linear-time algorithms exist, they use sophisticated data structures. We develop an algorithm for finding dominators that uses only a “static tree” disjoint set data structure in addition to simple lists and maps. The algorithm runs in near-linear or linear time, depending on the implementation of the disjoint set data structure. We give several versions of the algorithm, including one that computes loop nesting information (needed in many kinds of global code optimization) and that can be made self-certifying, so that the correctness of the computed dominators is very easy to verify.     

IMEP-24 analysis of eight trace elements in toys

The International Measurement Evaluation Program (IMEP) organised the IMEP-24 interlaboratory comparison after reports in the media about high levels of lead in toys. The aim of this comparison was to verify the laboratories’ capacity to evaluate trace-element levels in a possible toy-like material according to the European Standard EN 71-3:1994. As test material, it used a former certified reference material containing levels of antimony, arsenic, barium, cadmium, chromium, mercury, lead and selenium around the limits set in the standard.Four expert laboratories confirmed the reference values (Xref) for all elements but Hg, and established a reference value for Hg. The scatter of the results reported by the participants was large, as expected, but showed a close to normal distribution around the reference values for five of the eight trace elements. The spread of results was mainly attributed to sampling and sample preparation.One major issue observed in this exercise was the lack of legislative rules about how to report the result, or, more specifically, the use of the analytical correction, which was introduced in EN 71-3:1994 to achieve consistent interpretation of results and which is to be applied when values are equal to or above the maximum limits set in the standard. Its application by the participants was very inconsistent and led to problems in their evaluation. There is clearly a need for clarification and for more formal regulations with regard to result reporting in order to minimise the risk of confusion.Participants were also asked to give their opinion with regard to the acceptability of the test material for the market. The majority correctly considered the material as non-compliant. However, almost one-third incorrectly assessed the material as compliant.     

IMEP-24 analysis of eight trace elements in toys

The International Measurement Evaluation Program (IMEP) organized the IMEP-24 interlaboratory comparison after reports in the media about high levels of lead in toys. The aim of this comparison was to verify the laboratories’ capacity to evaluate trace-element levels in a possible toy-like material according to the European Standard EN 71-3:1994. As test material, it used a former certified reference material containing levels of antimony, arsenic, barium, cadmium, chromium, mercury, lead and selenium around the limits set in the standard.Four expert laboratories confirmed the reference values (Xref) for all elements but Hg, and established a reference value for Hg. The scatter of the results reported by the participants was large, as expected, but showed a close to normal distribution around the reference values for five of the eight trace elements. The spread of results was mainly attributed to sampling and sample preparation.One major issue observed in this exercise was the lack of legislative rules about how to report the result, or, more specifically, the use of the analytical correction, which was introduced in EN 71-3:1994 to achieve consistent interpretation of results and which is to be applied when values are equal to or above the maximum limits set in the standard. Its application by the participants was very inconsistent and led to problems in their evaluation. There is clearly a need for clarification and for more formal regulations with regard to result reporting in order to minimize the risk of confusion.Participants were also asked to give their opinion with regard to the acceptability of the test material for the market. The majority correctly considered the material as non-compliant. However, almost one-third incorrectly assessed the material as compliant.     

A polynomially bounded algorithm for a singly constrained quadratic program

This paper presents a characterization of the solutions of a singly constrained quadratic program. This characterization is then used in the development of a polynomially bounded algorithm for this class of problems.     

Entropy in linear programs

This paper treats entropy constrained linear programs from modelling as well as computational aspects. The optimal solutions to linear programs with one additional entropy constraint are expressed in terms of Lagrange-multipliers. Conditions for uniqueness are given. Sensitivity and duality are studied. The Newton—Kantorovich method is used to obtain a locally convergent iterative procedure. Related problems based on maximum entropy or minimum information are discussed.