Theorems of the Alternative and Optimization with Set-Valued Maps

In this paper, the concept of generalized cone subconvexlike set-valued mapsis presented and a theorem of alternative for the system of generalizedinequality–equality set-valued maps is established. By applying thetheorem of the alternative and other results, necessary and sufficientoptimality conditions for vector optimization problems with generalizedcone subconvexlike set-valued maps are obtained.     

多阶段应急决策的方案链选择方法

针对多阶段不同情景下多指标多任务的应急决策问题,提出了一种方案链选择方法。在该方法中,首先给出了决策方案链的概念,并对多阶段多指标多任务的应急决策问题进行了描述;然后根据相邻阶段的子方案之间的相容性,构建了相容性关系矩阵;进一步地,在考虑相邻阶段子方案之间相容性的情形下,以各阶段的子方案的综合评价值最大为目标,建立了应急决策的方案链选择的优化模型。通过求解模型,得到应急决策的最优方案链。最后,通过一个算例说明了该方法的可行性和有效性。     

Theorems of the Alternative for Inequality Systems of Real Polynomials

In this paper, we establish theorems of the alternative for inequality systems of real polynomials. For the real quadratic inequality system, we present two new results on the matrix decomposition, by which we establish two theorems of the alternative for the inequality system of three quadratic polynomials under an assumption that at least one of the involved forms be negative semidefinite. We also extend a theorem of the alternative to the case with a regular cone. For the inequality system of higher degree real polynomials, defined by even order tensors, a theorem of the alternative for the inequality system of two higher degree polynomials is established under suitable assumptions. As a byproduct, we give an equivalence result between two statements involving two higher degree polynomials. Based on this result, we investigate the optimality condition of a class of polynomial optimization problems under suitable assumptions.     

A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

Disbelieving the Normativity of Content

Adherents as well as detractors of the normativity of mental content agree that its assessment crucially depends on the assessment of a principle for believing what is true. In this paper, I present an alternative principle, which is based on possession conditions for pure thinking or mere entertaining. I argue that the alternative approach has not been sufficiently emphasised in the literature and has two important merits. First, it yields a direct analysis of the normativity of mental content, which is, furthermore, independent of arguably non-normative notions such as truth. Second, the approach suggests new and challenging lines of response to central non-normativist objections.     

An alternative tactic to deal with the contingency of driver absenteeism

On any given workday, unexpected absence of drivers calls for emergency operational tactics to ensure completion of planned deliveries of merchandise to customers. A typical tactic in the workforce scheduling literature is to rely exclusively on a pool of workers who were not scheduled for work; that is, full-time off-duty drivers and part-time drivers. Concerns about the expense of maintaining a staff of part-timers prompt consideration of alternative tactics. This study proposes one such alternative. It minimizes the part-time pool by reassigning routes among drivers who show for work. In multi-route vehicle routing problems, the prospect of this alternative arises because cost-minimizing patterns of travel distances across routes often allow one driver to do extra work by handling more than one route (subject to time-window and workload constraints). By considering costs such as overtime rates when drivers perform extra (emergency) driving duties and the cost to maintain part-time staff, this study tests the efficacy of the aforementioned alternative. Its efficacy is confirmed by the fact that it is less costly than the typical tactic: while the typical tactic adds just over 22% to driver payroll, the proposed alternative adds a noticeably smaller cost of just under 15%.     

A Proof of the Relaxation Theorem for Differential Inclusions Based on Euler Approximations

In this note, an alternative proof of the relaxation theorem is presented that is based on a two-level Euler approximation.     

An Interactive Approach for Choosing the Best of a Set of Alternatives

In this paper we address the problem of choosing the most preferred alternative among a large number of alternatives where each alternative is defined by multiple criteria. We assume that the decision maker has a quasiconcave utility function. We develop an exact approach that combines the ideas that have appeared in the literature regarding the use of different types of dummy alternatives in conjunction with real alternatives. Our experimental results indicate that the new approach is comparable to leading existing approaches.     

Theorems of the Alternative for Multivalued Mappings and Applications to Mixed Convex\Concave Systems of Inequalities

We provide a purely algebraic theorem of the alternative (and its topological variant) involving multivalued mappings under relaxed convexity assumptions. Various more or less classical applications are given, specially for nonconvex quadratic systems. In the second part of the paper we introduce an alternative formulation for a mixed convex\concave statement. The theory is applied to systems of mixed convex\concave inequalities.     

Statistical properties of the sample semi-variance

In finance theory the standard deviation of asset returns is almost universally recognized as a measure of risk. This universality continues to exist even in the presence of known limitations of using the standard deviation and also an extensive and growing literature on alternative risk measures. One possible reason for this persistence is that the sample properties of alternative risk measures are not well understood. This paper attempts to compare the sample distribution of the semi-variance with that of the variance. In particular, the belief that, while there are convincing theoretical reasons to use the semi-variance the volatility of the sample measure is so high as to make the measure impractical in applied work, is investigated. In addition arguments based on stochastic dominance are also used to compare the distribution of the two statistics. Conditions are developed to identify situations in which the semi-variance may be preferred to the variance. An empirical example using equity data from emerging markets demonstrates this approach.     

On generalized matrix approximation problem in the spectral norm

In this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the spectral norm are presented. An alternative solution expression for the generalized matrix approximation problem is obtained. This alternative expression provides a simple characterization of the achievable minimum rank, which is shown to be the same as the optimal objective value of the classical problem considered by Eckart–Young–Schmidt–Mirsky, as long as the generalized problem is feasible. In addition, this paper provides a result on a constrained version of the matrix approximation problem, establishing that the later problem is solvable via singular value decomposition.     

Skewness and the Beta Distribution

In this paper, alternative methods for estimating the beta distribution are proposed that utilize more information than the standard method based on the best, worst and most likely estimates. In particular, it is shown how information on skewness or the decision-maker's level of confidence can be incorporated into the estimation process. This provides an alternative to the restrictive assumptions that have to be made in the standard method. This is particularly useful when the skewness is expected to be high, or in situations where the degree of uncertainty is high.     

Theorems of the alternative and optimality conditions

A theorem of the alternative is stated for generalized systems. It is shown how to deduce, from such a theorem, known optimality conditions like saddle-point conditions, regularity conditions, known theorems of the alternative, and new ones. Exterior and interior penalty approaches, weak and strong duality are viewed as weak and strong alternative, respectively.     

Theorems of the alternative for conic integer programming

Farkas’ Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming. Its generalizations are known as theorems of the alternative. There exist theorems of the alternative for integer programming and conic programming. We present theorems of the alternative for conic integer programming. We provide a nested procedure to construct a function that characterizes feasibility over right-hand sides and can determine which statement in a theorem of the alternative holds.     

Implicit Finite--difference Solutions of the Enthalpy Formulation of Stefan Problems

When related to a phase-change problem, an implicit finite-differencediscretization of the enthalpy formulation results in a systemof non-linear equations at each time step. In this paper, variousnumerical enthalpy methods based on such discretizations areoutlined and examined. An alternative discretization for anenthalpy formulation is developed on separating the sensibleand latent heat terms. This approach also results in a non-linearsystem of equations but with the non-linearity isolated as asource term of nodal latent heat. This offers an advantage overthe previous techniques in that only one variable (i.e. temperature)is solved for in the resulting iterative scheme. Comparisonwith simple one- and two-dimensional test problems indicatethat the computing requirements, with the alternative discretization,are reduced by between 20 and 50%.     

面向多部门多属性的群决策应急方案调整方法

针对具有多部门多属性的基于案例推理的应急方案生成问题,提出了一种新的群决策应急方案调整方法。首先,各部门根据关注的属性生成案例库,并应用检索方法得到最相似历史案例,再运用置信规则库进行应急方案调整来生成各部门应急方案;然后,各部门对每个部门生成的应急方案进行评价;在此基础上,根据各部门的评价信息确定权重,进而对各部门生成的应急方案进行集结得到目标案例的应急方案。最后,通过一个算例验证了所提出方法的可行性和有效性。     

LMI优化问题的择一性定理与对偶

考虑目标函数是线性函数约束条件为线性矩阵不等式的LMI优化问题,讨论了LMI优化问题中的四个择一性定理.每种类型的择一性定理包含两个线性不等式和(或)等式系统,一个原始系统和一个对偶系统.弱择一性定理说明两系统中至多只有其一有解;基于凸集分离理论得到的强择一性定理说明两系统有且仅有其一有解.并在此基础上推导了LMI优化...     

The assessment of the information quality with the aid of multiple criteria analysis

The virtual business work flow depends on the information quality (IQ) which is essential attribute of information. The IQ depends strongly on organization of the information system (IS) and how the information is processed. In our approach we incorporate the four-aspect representation of IQ: (1) intrinsic, (2) contextual, (3) representational, and (4) accessibility. These four-aspects are divided into several criteria at the next level of hierarchy. The weights, representing the relative importance of criteria, have been assessed by pair-wise comparisons made by group of experts. Based on discussion with experts, six alternative strategies, that could be used for improving the IQ, were designed. For each given criterion, the group of subjects revealed the opinion about the level of achievement of every alternative. The set of scores, assigned to the alternative by different subjects, formed the discrete distribution that is used for a comparison of alternatives with the aid of stochastic dominances. In analogy to the Electre I methodology, the simple algorithm for the aggregate evaluation of analyzed alternatives was proposed. The benefits of proposed approach were demonstrated in a case study of the semiconductor industry. The results of our study suggest, that in case of matured company, the external strategies, that point out to the information exchange and strategic networked alliance with customers and suppliers, are preferred to the internal ones. The latter ones might be of greater importance for the new set up or for a young company.     

On optimization of the maintenance of a register

Data processing nowadays represents a considerable investment and it is important to use computers as efficiently as possible. Criteria separating the best alternative from other ones would be very useful.In this article we have tried to find some criteria for the optimization of register maintenance applying the simplest methods of operations research. In particular the use of a change register has been investigated.