Extensions of Dinkelbach's algorithm for solving non-linear fractional programming problems

Dinkelbach's algorithm was developed to solve convex fractinal programming. This method achieves the optimal solution of the optimisation problem by means of solving a sequence of non-linear convex programming subproblems defined by a parameter. In this paper it is shown that Dinkelbach's algorithm can be used to solve general fractional programming. The applicability of the algorithm will depend on the possibility of solving the subproblems. Dinkelbach's extended algorithm is a framework to describe several algorithms which have been proposed to solve linear fractional programming, integer linear fractional programming, convex fractional programming and to generate new algorithms. The applicability of new cases as nondifferentiable fractional programming and quadratic fractional programming has been studied. We have proposed two modifications to improve the speed-up of Dinkelbachs algorithm. One is to use interpolation formulae to update the parameter which defined the subproblem and another truncates the solution of the suproblem. We give sufficient conditions for the convergence of these modifications. Computational experiments in linear fractional programming, integer linear fractional programming and non-linear fractional programming to evaluate the efficiency of these methods have been carried out.     

Application of ultrasound technology in the drying of food products

This study presents a state-of-the-art overview on the application of ultrasound technology in the drying of food products, including the ultrasound pre-treatment and ultrasound assisted drying. The effect of main parameters and ultrasound technology on the drying kinetics and food quality were discussed. Inconsistencies were pointed out and analyzed in detail. Results showed that for ultrasound pre-treatment, the food products may lose or gain water and increase of ultrasonic parameters (sonication time, amplitude and ultrasound power) promoted the water loss or water gain. When ultrasound technology was applied prior to drying, an increase in drying kinetics was always observed, though some different results were also presented. For ultrasound assisted drying, the ultrasound power always gave a positive effect on the drying process, however, the magnitude of ultrasound improvement was largely dependent on the process variables, such as air velocity, air temperature, microwave power and vacuum pressure, etc. The application of ultrasound technology will somehow affect the food quality, including the physical and chemical ones. Generally, the ultrasound application can decrease the water activity, improve the product color and reduce the nutrient loss.     

Directional differentiability of the optimal value function in convex semi-infinite programming

In this paper, directional differentiability properties of the optimal value function of a parameterized semi-infinite programming problem are studied. It is shown that if the unperturbed semi-infinite programming problem is convex, then the corresponding optimal value function is directionally differentiable under mild regularity assumptions. A max-min formula for the directional derivatives, well-known in the finite convex case, is given.     

线性模型中参数向量的线性经验Bayes估计

本文利用线性经验Ｂａｙｅｓ估计的思想，对线性回归模型中未知参数向量构造了一类线性经验Ｂａｙｅｓ估计，并在一定条件下证明了其具有的ａ．ｏ．收敛速度．     

On Polyhedral Projection and Parametric Programming

This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the converse is tackled and it is shown how to formulate a PLP whose solution is the projection of an appropriately defined polyhedron described as the intersection of a finite number of halfspaces. The input to one operation can be converted to an input of the other operation and the resulting output can be converted back to the desired form in polynomial time—this implies that algorithms for computing projections or methods for solving parametric linear programs can be applied to either problem class. E.C. Kerrigan’s research was supported in part by the Royal Academy of Engineering, UK.     

Parametric mixed-integer 0–1 linear programming: The general case for a single parameter

Two algorithms for the general case of parametric mixed-integer linear programs (MILPs) are proposed. Parametric MILPs are considered in which a single parameter can simultaneously influence the objective function, the right-hand side and the matrix. The first algorithm is based on branch-and-bound on the integer variables, solving a parametric linear program (LP) at each node. The second algorithm is based on the optimality range of a qualitatively invariant solution, decomposing the parametric optimization problem into a series of regular MILPs, parametric LPs and regular mixed-integer nonlinear programs (MINLPs). The number of subproblems required for a particular instance is equal to the number of critical regions. For the parametric LPs an improvement of the well-known rational simplex algorithm is presented, that requires less consecutive operations on rational functions. Also, an alternative based on predictor–corrector continuation is proposed. Numerical results for a test set are discussed.     

Parametric multiple regression risk models: Theory and statistical analysis

Parametric multiple regression models for the claim number and the claim amount of an individual risk are introduced allowing explanatory variables to influence the mean claim number (amount). A model for an entire portfolio of risks is established on this basis. Then an extensive and in many cases efficient statistical analysis of this model is presented.     

Non-linear vibrations of parametrically excited cantilever beams subjected to non-linear delayed-feedback control

Non-linear feedback control provides an effective methodology for vibration mitigation in non-linear dynamic systems. However, within digital circuits, actuation mechanisms, filters, and controller processing time, intrinsic time-delays unavoidably bring an unacceptable and possibly detrimental delay period between the controller input and real-time system actuation. If not well-studied, these inherent and compounding delays may inadvertently channel energy into or out of a system at incorrect time intervals, producing instabilities and rendering controllers’ performance ineffective. In this work, we present a comprehensive investigation of the effect of time delays on the non-linear control of parametrically excited cantilever beams. More specifically, we examine three non-linear cubic delayed-feedback control methodologies: position, velocity, and acceleration delayed feedback. Utilizing the method of multiple scales, we derive the modulation equations that govern the non-linear dynamics of the beam. These equations are then utilized to investigate the effect of time delays on the stability, amplitude, and frequency–response behavior. We show that, when manifested in the feedback, even the minute amount of delays can completely alter the behavior and stability of the parametrically excited beam, leading to unexpected behavior and responses that could puzzle researchers if not well-understood and documented.     

Nonlinear Phase Shift by Parametric Amplification in Leaky Waveguides

In this article, the cascaded second-order nonlinear phase shifts induced in the signal wave are studied using the three-wave parametric interaction in a four-layered QPM leaky waveguide configuration in Z-cut LiNbO 3 . In this interaction, the pump-andsignal waves are guided modes and the idler is radiated into the substrate. We have analyzed the nonlinear phase shifts induced in the signal wave due to cascaded second-order effects, as a function of different waveguide parameters. These studies should find application in realizing practical all-optical signal processing devices.     

共同均值矩阵的线性估计的泛容许性

本文给出了多元线性模型中共同均值矩阵可估函数的线性估计的泛容许性定义,并得到了共同均值矩阵可估函数的线性估计分别在齐次和非齐次线性估计类中的泛容许性特征。