Exact approaches for testing non-inferiority or superiority of two incidence rates

We studied an unconditional approach based on partial maximization using different penalty values for comparing two incidence rates from Poisson distributions. We also consider a full maximization approach and an approach based on estimation and full maximization. Generally, the third approach has good performance.     

A distribution-free approach to estimating best response values with application to mutual fund performance modeling

Frontier regression models seek to model and estimate best rather than average values of a response variable. Our proposed frontier model has similar intent, but also allows for an additional error term. The composed error approach uses the sum of two error terms, one an inefficiency error and the other as white noise. Previous research proposed assumptions on the distributions of the error components so that the distribution of this total error can be specified. Here we propose a distribution free approach to specifying these errors. In addition, our approach is completely data driven, rendering model specification an unnecessary step. We also outline, step-by-step, an approach to implementing this procedure. Our entire approach is illustrated with a mutual fund data set from the Morning Star database.     

A note on solving MINLP’s using formulation space search

In this note we present an approach based on formulation space search to solve mixed-integer nonlinear (zero-one) programming problems. Our approach is an iterative one which adds a single nonlinear inequality constraint of increasing tightness to the original problem. Computational results are presented for our approach on 51 standard benchmark problems taken from MINLPLib. We compare our approach against the Minotaur and minlp_bb nonlinear solvers, as well as against the RECIPE algorithms.     

An approach for solving nonlinear multi-objective separable discrete optimization problem with one constraint

We propose an exact solution approach for solving nonlinear multi-objective optimization problems with separable discrete variables and a single constraint. The approach converts the multi-objective problem into a single objective problem by using surrogate multipliers from which we find all the solutions with objective values within a given range. We call this the surrogate target problem which is solved by using an algorithm based on the modular approach. Computational experiments demonstrate the effectiveness of this approach in solving large-scale problems. A simple example is presented to illustrate an interactive decision making process.     

Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem

This paper proposes a new linear programming approach to solve the two-group classification problem in discriminant analysis. This new approach is based on an idea from cluster analysis that objects within the same group should be more similar than objects between groups. Consequently, it is desirable for the classification score of an object to be nearer to its mean classification score, but further from the mean classification score of the other group. This objective is accomplished by minimizing the total deviation of the classification scores of the objects from their group mean scores in a linear programming approach. When applied to an actual managerial problem and simulated data, the proposed linear programming approach performs well both in groups separation and group-membership predictions of new objects. Moreover, this new approach has an advantage of obtaining more stable classification function across different samples than most of the existing linear programming approaches.     

关于线性二层规划分枝定界方法的探讨

对求解线性二层规划的分枝定界方法进行了探讨.给出的一个例子表明,目前的分枝定界方法不能很好地解决上层带有任意线性形式约束的线性二层规划问题,进而在线性二层规划新定义的基础上提出了求解线性二层规划的扩展分枝定界方法.算例表明扩展分枝定界方法可以有效解决原分枝定界方法的不足.     

The exponentialization approach to flexible manufacturing system models with general processing times

Recently flexible manufacturing systems (FMSs) have been modelled as closed networks of queues. In this paper we develop an exponentialization approach to the modeling of FMS networks with general processing times. The idea of the approach is to transform the network into an (approximately) equivalent exponential network, where each station has exponential processing times with state-dependent rates. The approach is formulated as a fixed-point problem. Numerical examples have indicated excellent accuracies of the approach. This approach can also be readily adapted to accommodate limited local buffers and dynamic parts routing.     

Multi-objective tabu search using a multinomial probability mass function

A tabu search approach to solve multi-objective combinatorial optimization problems is developed in this paper. This procedure selects an objective to become active for a given iteration with a multinomial probability mass function. The selection step eliminates two major problems of simple multi-objective methods, a priori weighting and scaling of objectives. Comparison of results on an NP-hard combinatorial problem with a previously published multi-objective tabu search approach and with a deterministic version of this approach shows that the multinomial approach is effective, tractable and flexible.     

A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems

Inspired by the reduced basis approach and modern numerical multiscale methods, we present a new framework for an efficient treatment of heterogeneous multiscale problems. The new approach is based on the idea of considering heterogeneous multiscale problems as parametrized partial differential equations where the parameters are smooth functions. We then construct, in an offline phase, a suitable localized reduced basis that is used in an online phase to efficiently compute approximations of the multiscale problem by means of a discontinuous Galerkin method on a coarse grid. We present our approach for elliptic multiscale problems and discuss an a posteriori error estimate that can be used in the construction process of the localized reduced basis. Numerical experiments are given to demonstrate the efficiency of the new approach.     

A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis

Based on the equilibrium efficient frontier data envelopment analysis (EEFDEA) approach, Fang (J Oper Res Soc 67:412–420, 2015a) developed an equivalent linear programming model to improve and strengthen the EEFDEA approach. Furthermore, Fang (2015a) indicated that his secondary goal approach can achieve a unique equilibrium efficient frontier. However, through a simple counterexample we demonstrate that Fang’s secondary goal approach cannot always achieve uniqueness of the equilibrium efficient frontier. In this paper, we propose an algorithm based on the secondary goal approach to address the problem. The proposed algorithm is proven mathematically to be an effective approach to guaranteeing the uniqueness of the equilibrium efficient frontier.     

RM approach for ranking of generalized trapezoidal fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).     

Possibilistic signal processing: How to handle noise?

We propose a novel approach for noise quantifier at each location of a signal. This method is based on replacing the conventional kernel-based approach extensively used in signal processing by an approach involving another kind of kernel: a possibility distribution. Such an approach leads to interval-valued resulting methods instead of point-valued ones. We propose a theoretical justification to this approach and we show, on real and artificial data sets, that the length of the obtained interval and the local noise level are highly correlated. This method is non-parametric and has an advantage over other methods since no assumption about the nature of the noise has to be made, except its local ergodicity. Besides, the propagation of the noise in the involved signal processing method is direct and does not require any additional computation.     

Frequently hypercyclic subspaces

We study the existence of frequently hypercyclic subspaces for a given operator, that is, the existence of closed infinite-dimensional subspaces in which every non-zero vector is frequently hypercyclic. We attack the problem with any of the three methods that have been used for hypercyclic subspaces: a constructive approach, an approach via left-multiplication operators, and an approach via tensor products.     

Discrete and continuous methods in ballistics

The kinematics of a projectile in flight provides an ideal opportunity for an introduction to (and a comparison between) discrete and continuous methods in applied mathematics. We use a graphical method in the discrete approach, which provides good physical insight and serves as an introduction to finite difference methods. The continuous approach is better in the no‐drag case, but the discrete approach is foundto be more effective when a nonlinear drag effect is included in the model.     

An Approach to Finding a Global Minimization with Equality and Inequality Constraints

We give an approach for finding a global minimization with equality and inequality Constraints.Our approach is to construct an exact penalty function, and prove that the global minimal points of this exact penalty function are the primal constrained global minimal points. Thus we convert the problem of global constrained optimization into a problem of global unconstrained optimization. Furthermore, the integral approach for finding a global minimization for a class of discontinuous functions is used and an implementable algorithm is given.     

Quantified functional analysis: recapturing the dual unit ball

We introduce the weak approach structure for an arbitrary locally convex approach space and generalize the results from [1] about the weak approach structure of a normed space. Hereto we carefully develop the notion of a closed dual unit ball in an abstract setting (as a special kind of absolutely convex subset) because it is this kind of structure on the algebraic dual that induces, in a duality-compatible way, a locally convex approach structure on the original space.     

A receding horizon D-optimization approach for model identification–oriented input design and application in combustion engines

In this paper, a receding horizon D-optimization approach for model identification–oriented input design is proposed, and a practical application is demonstrated for internal combustion engines. The proposed approach consists of a recursive parameter identification algorithm and an input signal design algorithm; where the latter provides D-optimal excitation signal for the adaptation of the parameter estimation in the following identification phase. The D-optimization algorithm is constructed with the Continuation/GMRES method, which provides an approximate solution according to the current parameter of the model. To validate effectiveness and feasibility of the proposed approach, testing results applying the proposed approach to an internal combustion engine are demonstrated and conducted on a full-scale engine test bench.     

Implementing a flipped classroom approach in a university numerical methods mathematics course

This paper describes and analyses the implementation of a ‘flipped classroom’ approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an examination of the attitudes of the 2014 cohort to the approach in general as well as analysing their use of the videos. Based on these responses, the instructor makes a number of changes (for example, the use of ‘cloze’ summary notes and the introduction of an extra, optional tutorial class) before repeating the ‘flipped classroom’ approach the following year. The attitudes to the approach and the video usage of the 2015 cohort are then compared with the 2014 cohort and further changes that could be implemented for the next cohort are suggested.     

On the Laplacian spectrum of an infinite graph

In this paper, we introduce the notion of Laplacian spectrum of an infinite countable graph in a different way than in the papers by B. Mohar. We prove some basic properties of this type of spectrum. The approach used is in line with our approach to the limiting spectrum of an infinite graph. The technique of the Laplacian spectrum of finite graphs is essential in this approach.     

A numerical scheme for a class of nonlinear Fredholm integral equations of the second kind

In this paper an iterative approach for obtaining approximate solutions for a class of nonlinear Fredholm integral equations of the second kind is proposed. The approach contains two steps: at the first one, we define a discretized form of the integral equation and prove that by considering some conditions on the kernel of the integral equation, solution of the discretized form converges to the exact solution of the problem. Following that, in the next step, solution of the discretized form is approximated by an iterative approach. We finally on some examples show the efficiency of the proposed approach.