Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

The paper is devoted to solving the two‐stage problem of stochastic programming with quantile criterion. It is assumed that the loss function is bilinear in random parameters and strategies, and the random vector has a normal distribution. Two algorithms are suggested to solve the problem, and they are compared. The first algorithm is based on the reduction of the original stochastic problem to a mixed integer linear programming problem. The second algorithm is based on the reduction of the problem to a sequence of convex programming problems. Performance characteristics of both the algorithms are illustrated by an example. A modification of both the algorithms is suggested to reduce the computing time. The new algorithm uses the solution obtained by the second algorithm as a starting point for the first algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Mesh and solver co‐adaptation in finite element methods for anisotropic problems

Mesh generation and algebraic solver are two important aspects of the finite element methodology. In this article, we are concerned with the joint adaptation of the anisotropic triangular mesh and the iterative algebraic solver. Using generic numerical examples pertaining to the accurate and efficient finite element solution of some anisotropic problems, we hereby demonstrate that the processes of geometric mesh adaptation and the algebraic solver construction should be adapted simultaneously. We also propose some techniques applicable to the co‐adaptation of both anisotropic meshes and linear solvers. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Mathematical model for the dynamics of visceral leishmaniasis–malaria co‐infection

A mathematical model to understand the dynamics of malaria–visceral leishmaniasis co‐infection is proposed and analyzed. Results show that both diseases can be eliminated if R₀, the basic reproduction number of the co‐infection, is less than unity, and the system undergoes a backward bifurcation where an endemic equilibrium co‐exists with the disease‐free equilibrium when one of R_m or R_l, the basic reproduction numbers of malaria‐only and visceral leishmaniasis‐only, is precisely less than unity. Results also show that in the case of maximum protection against visceral leishmaniasis (VL), the disease‐free equilibrium is globally asymptotically stable if malaria patients are protected from VL infection; similarly, in the case of maximum protection against malaria, the disease‐free equilibrium is globally asymptotically stable if VL and post‐kala‐azar dermal leishmaniasis patients and the recovered humans after VL are protected from malaria infection. Numerical results show that if R_m and R_l are greater than unity, then we have co‐existence of both disease at an endemic equilibrium, and malaria incidence is higher than visceral leishmaniasis incidence at steady state. Copyright © 2016 John Wiley & Sons, Ltd.     

Affine,quasi‐affine and co‐affine frames on local fields of positive characteristic

The concept of quasi‐affine frame in Euclidean spaces was introduced to obtain translation invariance of the discrete wavelet transform. We extend this concept to a local field K of positive characteristic. We show that the affine system generated by a finite number of functions is an affine frame if and only if the corresponding quasi‐affine system is a quasi‐affine frame. In such a case the exact frame bounds are equal. This result is obtained by using the properties of an operator associated with two such affine systems. We characterize the translation invariance of such an operator. A related concept is that of co‐affine system. We show that there do not exist any co‐affine frame in .     

BFGS‐like updates of constraint preconditioners for sequences of KKT linear systems in quadratic programming

We focus on efficient preconditioning techniques for sequences of Karush‐Kuhn‐Tucker (KKT) linear systems arising from the interior point (IP) solution of large convex quadratic programming problems. Constraint preconditioners (CPs), although very effective in accelerating Krylov methods in the solution of KKT systems, have a very high computational cost in some instances, because their factorization may be the most time‐consuming task at each IP iteration. We overcome this problem by computing the CP from scratch only at selected IP iterations and by updating the last computed CP at the remaining iterations, via suitable low‐rank modifications based on a BFGS‐like formula. This work extends the limited‐memory preconditioners (LMPs) for symmetric positive definite matrices proposed by Gratton, Sartenaer and Tshimanga in 2011, by exploiting specific features of KKT systems and CPs. We prove that the updated preconditioners still belong to the class of exact CPs, thus allowing the use of the conjugate gradient method. Furthermore, they have the property of increasing the number of unit eigenvalues of the preconditioned matrix as compared with the generally used CPs. Numerical experiments are reported, which show the effectiveness of our updating technique when the cost for the factorization of the CP is high.     

Studying the emerging global brain: Analyzing and visualizing the impact of co‐authorship teams

This article introduces a suite of approaches and measures to study the impact of co‐authorship teams based on the number of publications and their citations on a local and global scale. In particular, we present a novel weighted graph representation that encodes coupled author‐paper networks as a weighted co‐authorship graph. This weighted graph representation is applied to a dataset that captures the emergence of a new field of science and comprises 614 articles published by 1036 unique authors between 1974 and 2004. To characterize the properties and evolution of this field, we first use four different measures of centrality to identify the impact of authors. A global statistical analysis is performed to characterize the distribution of paper production and paper citations and its correlation with the co‐authorship team size. The size of co‐authorship clusters over time is examined. Finally, a novel local, author‐centered measure based on entropy is applied to determine the global evolution of the field and the identification of the contribution of a single author's impact across all of its co‐authorship relations. A visualization of the growth of the weighted co‐author network, and the results obtained from the statistical analysis indicate a drift toward a more cooperative, global collaboration process as the main drive in the production of scientific knowledge. © 2005 Wiley Periodicals, Inc. Complexity 10: 57–67, 2005     

High‐performance direct algorithms for computing the sign function of triangular matrices

Algorithms and implementations for computing the sign function of a triangular matrix are fundamental building blocks for computing the sign of arbitrary square real or complex matrices. We present novel recursive and cache‐efficient algorithms that are based on Higham's stabilized specialization of Parlett's substitution algorithm for computing the sign of a triangular matrix. We show that the new recursive algorithms are asymptotically optimal in terms of the number of cache misses that they generate. One algorithm that we present performs more arithmetic than the nonrecursive version, but this allows it to benefit from calling highly optimized matrix multiplication routines; the other performs the same number of operations as the nonrecursive version, suing custom computational kernels instead. We present implementations of both, as well as a cache‐efficient implementation of a block version of Parlett's algorithm. Our experiments demonstrate that the blocked and recursive versions are much faster than the previous algorithms and that the inertia strongly influences their relative performance, as predicted by our analysis.     

Iterative algorithms for finding minimum‐norm fixed point of nonexpansive mappings and applications

This paper deals with the problem of finding minimum‐norm fixed point of nonexpansive mappings. We present two types of iteration methods (one is implicit, and the other is explicit). We establish strong convergence theorems for both methods. Some applications are given regarding convex optimization problems and split feasibility problems. These results improve some known results existing in the literatures. Copyright © 2013 John Wiley & Sons, Ltd.     

Supercritical Neimark‐Sacker bifurcation of a discrete‐time Nicholson‐Bailey model

We study the local dynamics and supercritical Neimark‐Sacker bifurcation of a discrete‐time Nicholson‐Bailey host‐parasitoid model in the interior of . It is proved that if α>1, then the model has a unique positive equilibrium point , which is locally asymptotically focus, unstable focus and nonhyperbolic under certain parametric condition. Furthermore, it is proved that the model undergoes a supercritical Neimark‐Sacker bifurcation in a small neighborhood of the unique positive equilibrium point , and meanwhile, the stable closed curve appears. From the viewpoint of biology, the stable closed curve corresponds to the period or quasiperiodic oscillations between host and parasitoid populations. Some numerical simulations are presented to verify theoretical results.     

High‐order algorithms for Riesz derivative and their applications (V)

In this article, based on the idea of combing symmetrical fractional centred difference operator with compact technique, a series of even‐order numerical differential formulas (named the fractional‐compact formulas) are established for the Riesz derivatives with order . Properties of coefficients in the derived formulas are studied in details. Then applying the constructed fourth‐order formula, a difference scheme is proposed to solve the Riesz spatial telegraph equation. By the energy method, the constructed numerical algorithm is proved to be stable and convergent with order , where τ and h are the temporal and spatial stepsizes, respectively. Finally, several numerical examples are presented to verify the theoretical results.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1754–1794, 2017     

Dynamical behavior of fractional‐order energy‐saving and emission‐reduction system and its discretization

This paper attempts to explore dynamical behavior and mathematical properties of the three‐dimensional fractional‐order energy‐saving and emission‐reduction system. Theoretically, the conditions of local stability of fractional‐order system's equilibrium points are obtained. Numerical investigations on the dynamics of this system are carried out, and the existence of the asymptotically stable attractor is found. Combined with the fractional‐order subsystem, we discuss the relationship between energy‐saving and emission‐reduction and economic growth, and carbon emissions and economic growth. Furthermore, we discretize the fractional‐order system and give necessary and sufficient conditions of its stabilization. It is shown that the stability of the discretization system is impacted by the system's fractional parameter. Numerical simulations show the richer dynamical behavior of the fractional‐order system and verify the theoretical results. Recommendations for Resource Managers

• The impact of carbon emissions on economic growth is one of the main reasons for energy‐saving and emission‐reduction.
• Control measures on people's low‐carbon life through government intervention are required to protect the natural environment.
• New energy‐saving and emission‐reduction technologies should be implemented to achieve sustainable social and economic development.

     

Reduction of the bilevel stochastic optimization problem with quantile objective function to a mixed‐integer problem

The paper is devoted to the stochastic optimistic bilevel optimization problem with quantile criterion in the upper level problem. If the probability distribution is finite, the problem can be transformed into a mixed‐integer nonlinear optimization problem. We formulate assumptions guaranteeing that an optimal solution exists. A production planning problem is used to illustrate usefulness of the model. Copyright © 2017 John Wiley & Sons, Ltd.     

P‐moment stability under small Gauss type random excitation of stochastic system

In this paper, the stochastic stability under small Gauss type random excitation is investigated theoretically and numerically. When p is larger than 0, the p‐moment stability theorem of stochastic models is proved by Lyapunov method, Ito isometry formula, matrix theory and so on. Then the application of p‐moment such as k‐order moment of the origin and k‐order moment of the center is introduced and analyzed. Finally, p‐moment stability of the power system is verified through the simulation example of a one machine and infinite bus system. Copyright © 2016 John Wiley & Sons, Ltd.     

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.     

Strong convergence of the split‐step θ‐method for stochastic age‐dependent population equations

In this paper, we constructed the split‐step θ (SSθ)‐method for stochastic age‐dependent population equations. The main aim of this paper is to investigate the convergence of the SS θ‐method for stochastic age‐dependent population equations. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from the theory, and comparative analysis with Euler method is given, the results show the higher accuracy of the SS θ‐method. Copyright © 2014 John Wiley & Sons, Ltd.     

Stochastic models for air cargo terminal manpower supply planning in long‐term operations

In this research, based on two deterministic‐demand planning models, we established two long‐term stochastic‐demand planning models by incorporating the stochastic disturbances of manpower demands that occur in actual operations. The models are formulated as mixed integer linear programs that are solved using a mathematical programming solver. To compare the performance of the two stochastic‐demand and two deterministic‐demand planning models under the stochastic demands that occur in actual operations, we further develop a simulation‐based evaluation method. Finally, we perform numerical tests using real operating data from a Taiwan air cargo terminal. The preliminary results show that the stochastic models could be useful for planning air cargo terminal manpower supply. Copyright © 2008 John Wiley & Sons, Ltd.     

Two types of upper semi‐continuity of bi‐spatial attractors for non‐autonomous stochastic p‐Laplacian equations on

We consider the long time behavior of solutions for the non‐autonomous stochastic p‐Laplacian equation with additive noise on an unbounded domain. First, we show the existence of a unique ‐pullback attractor, where q is related to the order of the nonlinearity. The main difficulty existed here is to prove the asymptotic compactness of systems in both spaces, because the Laplacian operator is nonlinear and additive noise is considered. We overcome these obstacles by applying the compactness of solutions inside a ball, a truncation method and some new techniques of estimates involving the Laplacian operator. Next, we establish the upper semi‐continuity of attractors at any intensity of noise under the topology of . Finally, we prove this continuity of attractors from domains in the norm of , which improves an early result by Bates et al.(2001) who studied such continuity when the deterministic lattice equations were approached by finite‐dimensional systems, and also complements Li et al. (2015) who discussed this approximation when the nonlinearity f(·,0) had a compact support. Copyright © 2017 John Wiley & Sons, Ltd.     

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

An n × n real matrix A = (a_ij)_{n × n} is called bi‐symmetric matrix if A is both symmetric and per‐symmetric, that is, a_ij = a_ji and a_ij = a_n+1?1,n+1?i (i, j = 1, 2,..., n). This paper is mainly concerned with finding the least‐squares bi‐symmetric solutions of matrix inverse problem AX = B with a submatrix constraint, where X and B are given matrices of suitable sizes. Moreover, in the corresponding solution set, the analytical expression of the optimal approximation solution to a given matrix A^* is derived. A direct method for finding the optimal approximation solution is described in detail, and three numerical examples are provided to show the validity of our algorithm. Copyright © 2007 John Wiley & Sons, Ltd.     

A stochastic model for a general load‐sharing system under overload condition

A load‐sharing parallel system functions if at least one unit in the system is functioning and the surviving units share the load. In most of research on load‐sharing system, the performance of the system has been studied only for the case when the lifetimes of components in the system follow exponential distributions. In this paper a load‐sharing parallel system is considered when the lifetimes of the units in the system are any continuous random variables. The reliability function of the system is derived and the problem of load allocation is also considered. Copyright © 2009 John Wiley & Sons, Ltd.     

The improved split‐step θ methods for stochastic differential equation

Two improved split‐step θ methods, which, respectively, named split‐step composite θ method and modified split‐step θ‐Milstein method, are proposed for numerically solving stochastic differential equation of Itô type. The stability and convergence of these methods are investigated in the mean‐square sense. Moreover, an approach to improve the numerical stability is illustrated by choices of parameters of these two methods. Some numerical examples show the accordance between the theoretical and numerical results. Further numerical tests exhibit not only the Hamiltonian‐preserving property of the improved split‐step θ methods for a stochastic differential system but also the positivity‐preserving property of the modified split‐step θ‐Milstein method for the Cox–Ingersoll–Ross model. Copyright © 2013 John Wiley & Sons, Ltd.