Maximal domains of quasi-convexity and pseudo-convexity for quadratic functions

We study quasi-convex and pseudo-convex quadratic functions on solid convex sets. This generalizes Martos' results in [12] and [13] by using Koecher's results in [8].This research was supported by Hydro—Quebec; University of Montreal; Office of Naval Research, Contract N-00014-47-A0112-0011; National Science Foundation, Grant GP 25738.     

Building the Additive Utility Functions for CAD-UFRJ Evaluation Staff Criteria

This paper presents an application of the UTA method for building utility functions for the evaluation criteria defined by the Staff Evaluation Commission (CAD) of the Rio de Janeiro Federal University (UFRJ). Every year, the CAD-UFRJ gives the staff evaluation results for each Postgraduate Engineering Programme. However, the method used to generate the staff evaluation is assumed unknown. Trying to find the CAD-UFRJ preference structure, the evaluation results supplied by CAD-UFRJ are used to apply the UTA method. Some additional information obtained from the CAD-UFRJ data is incorporated in the optimal solutions analysis.     

Non-differentiable pseudo-convex functions and duality for minimax programming problems

Optimality results are derived for a general minimax programming problem under non-differentiable pseudo-convexity assumptions. A dual in terms of Dini derivatives is introduced and duality results are established. Finally, two duals again in terms of Dini derivatives are introduced for a generalized fractional minimax programming problem and corresponding results are studied.     

The self regulation problem as an inexact steepest descent method for multicriteria optimization

In this paper we study an inexact steepest descent method for multicriteria optimization whose step-size comes with Armijo’s rule. We show that this method is well-defined. Moreover, by assuming the quasi-convexity of the multicriteria function, we prove full convergence of any generated sequence to a Pareto critical point. As an application, we offer a model for the Psychology’s self regulation problem, using a recent variational rationality approach.     

Procurement strategies for lost-sales inventory systems with all-units discounts

Despite the prevalence of all-units discounts in procurement contracts, these discounts pose a technical challenge to analyze procurement strategies due to neither concave nor convex ordering costs. In this paper, we consider the optimal procurement strategies with all-units discounts under the lost-sales setting. By assuming log-concave demands, we find that the optimal procurement strategies have a generalized Q-jump (s, S) structure by introducing a new notion of Q-jump single-crossing. In particular, a sufficient condition is provided for degenerating the optimal procurement strategies from a generalized Q-jump (s, S) structure into a Q-jump (s, S) structure, which is definitely optimal for the single-period problem. Extensive numerical results suggest that the Q-jump (s, S) policy as a heuristic performs considerably well when its optimality sufficient condition is violated. Our results can be extended to systems with multi-break all-units discounts, and systems with all-units discounts on batch ordering.     

Multivalued convexity and optimization: A unified approach to inequality and equality constraints

Multivalued functions satisfying a general convexity condition are examined in the first section. The second section establishes a general transposition theorem for such functions and develops an abstract multiplier principle for them. In particular both convex inequality and linear equality constraints are seen to satisfy the same generalized constraint qualification. The final section examines quasi-convex programmes.     

基于准则间关系的多准则语言决策方法

在多准则语言决策问题中,准则间的关系一般有三种:相互独立、相互影响、优先关系.基于这三种关系,结合比例二元组语义信息提出了一种新的多准则语言决策方法.介绍了比例二元组优先加权平均(P2TPWA)算子,并讨论了有关P2TPWA算子的相关性质.另外,将Choquet积分拓展到了比例二元组语言环境,并将P2TPWA算子和比例二元组语言Choquet积分用于实际的决策问题中.     

Digital Tools for Algebra Education: Criteria and Evaluation

In the Netherlands, as in many other countries, the algebraic expertise of students graduating from secondary education is an issue. The use of digital tools for algebra education is expected to change epistemologies, activity structures and student achievement. Therefore, a study was set up to investigate in what way the use of ICT in upper secondary education might enhance the algebraic expertise of students. One of the first decisions to be made concerned the choice of appropriate digital tools. This paper describes the process of designing and using an instrument for evaluating digital tools. The conceptual framework guiding this process includes notions on symbol sense, instrumental genesis and formative assessment. The evaluation instrument is designed through a Delphi method and provides a blueprint of tool features that are relevant for the purpose of this study. The results show that such an evaluation instrument is valuable both for choosing appropriate digital tools and for making concrete the aims and expectations that researchers have on the issue of integrating technology in algebra education. The final instrument is presented and illustrated through examples implemented in different digital algebra tools.     

A sequential method for nonlinear filtering: Numerical implementation and comparisons

Exact equations are presented for sequentially updating the optimal solution for a discrete-time analog of the basic Sridhar nonlinear filtering problem as the process length increases and new observations are obtained. A tabular method is described for implementing numerically the sequential filtering equations. The accuracy and efficiency of the tabular method are illustrated by means of several numerical examples.Dedicated to R. SridharThe work of R. Kalaba and L. Tesfatsion was partially supported by the National Science Foundation under Grant No. ENG-77-28432 and by the National Institutes of Health under Grant No. GM-23732-03.     

逆矩阵的判定及计算方法

线性代数是大学教育中一门难度较高的基础必修课程,而逆矩阵是教学过程中一个主要概念,对研究其他线性结构有着非常重要的作用.本文通过对逆矩阵定义的分析,汇总若干个判定矩阵是否可逆的方法,同时提供了多种逆矩阵的计算技巧,包括利用计算机技术简化繁琐的计算过程,这些都是学习者在学习过程中需要掌握的重要内容.本文旨在协助教师在开展教学时,能够举一反三,以点带面来引导学生将所学知识融合,注重知识点之间的相关性学习;同时,也帮助学习者能够更加全面的认识逆矩阵这一重要概念.     

Performance comparisons for maintained items

Most maintenance studies deal with the problem of maintenance-costs optimization, given the cost of the available maintenance actions and a cost objective function. The focus in this paper is on yet another relevant aspect namely the improvement in performance that results from a maintenance action in terms of performance criteria of interest. The evaluation of performance improvement requires comparisons of random quantities which is done by means of suitable probabilistic ordering notions. Different modelling situations are considered, and for each of them conditions are obtained on the life distributions of the present item, and the new one if of different type, that ensure performance improvement. Apart from providing a decision tool for maintenance application, the paper also contributes to clarifying relationships between (probabilistic) ordering notions and aging properties within the maintenance context.     

Stochastic comparisons for bulk queues

We consider two important classes of single-server bulk queueing models: M^(X)/G^(Y)/1 with Poisson arrivals of customer groups, and G^(X)/m^(Y)1 with batch service times having exponential density. In each class we compare two systems and prove that one is more congested than the other if their basic random variables are stochastically ordered in an appropriate manner. However, it must be recognized that a system that appears congested to customers might be working efficiently from the system manager's point of view. We apply the results of this comparison to (i) the family {M/G^(s)/1,s 1} of systems with Poisson input of customers and batch service times with varying service capacity; (ii) the family {G^(s)/1,s 1} of systems with exponential customer service time density and group arrivals with varying group size; and (iii) the family {M/D/s,s 1} of systems with Poisson arrivals, constant service time and varying number of servers. Within each family, we find the system that is the best for customers, but this turns out to be the worst for the manager (or vice versa). We also establish upper (or lower) bounds for the expected queue length in steady state and the expected number of batches (or groups) served during a busy period. The approach of the paper is based on the stochastic comparison of random walks underlying the models.This research was partially supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.     

Criteria for -ampleness

In the noncommutative geometry of Artin, Van den Bergh, and others, the twisted homogeneous coordinate ring is one of the basic constructions. Such a ring is defined by a -ample divisor, where is an automorphism of a projective scheme . Many open questions regarding -ample divisors have remained.

We derive a relatively simple necessary and sufficient condition for a divisor on to be -ample. As a consequence, we show right and left -ampleness are equivalent and any associated noncommutative homogeneous coordinate ring must be noetherian and have finite, integral GK-dimension. We also characterize which automorphisms yield a -ample divisor.

     

H-张量的判定及其应用

H-张量在科学和工程实际中具有重要应用,但在实际中要判定H-张量是比较困难的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出了一些比较实用的新条件.作为应用,给出判定偶数阶实对称张量正定性的条件,相应数值例子说明了结果的有效性.     

非奇异H-矩阵的判定准则(英文)

本文中,给出了非奇异H-矩阵的新判定条件,改进了近期的相关结果,并用数值例子说明了所得结果判定范围的更加广泛性。     

Criteria for strong H-tensors

H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.     

Some comparisons for Gaussian processes

Extensions and variants are given for the well-known comparison principle for Gaussian processes based on ordering by pairwise distance.

     

Criteria for Componentwise Linearity

We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals generated by the submaximal minors of a symmetric matrix.     

Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons

At the intersection of nonlinear and combinatorial optimization, quadratic programming has attracted significant interest over the past several decades. A variety of relaxations for quadratically constrained quadratic programming (QCQP) can be formulated as semidefinite programs (SDPs). The primary purpose of this paper is to present a systematic comparison of SDP relaxations for QCQP. Using theoretical analysis, it is shown that the recently developed doubly nonnegative relaxation is equivalent to the Shor relaxation, when the latter is enhanced with a partial first-order relaxation-linearization technique. These two relaxations are shown to theoretically dominate six other SDP relaxations. A computational comparison reveals that the two dominant relaxations require three orders of magnitude more computational time than the weaker relaxations, while providing relaxation gaps averaging 3% as opposed to gaps of up to 19% for weaker relaxations, on 700 randomly generated problems with up to 60 variables. An SDP relaxation derived from Lagrangian relaxation, after the addition of redundant nonlinear constraints to the primal, achieves gaps averaging 13% in a few CPU seconds.