EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

A branch-and-bound algorithm for multi-dimensional quadratic 0-1 knapsack problems

In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions. The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds was determined with the outer approximation method. Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems.

Relaxation-strategy-based Modification Branch-and-Bound Algorithm for Solving a Class of Transportation-production Problems

In this paper,a new algorithm relaxation-strategy-based modification branchand-bound algorithm is developed for a type of solving the minimum cost transportationproduction problem with concave production costs.The major improvement of the proposed new method is that modification algorithm reinforces the bounding operation using a Lagrangian relaxation,which is a concave minimization but obtains a tighter bound than the usual linear programming relaxation.Some computational results are included.Computation results indicate that the algorithm can solve fairly large scale problems.

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function space L2 on the boundary manifold. Then an easy example of several variables, the version of torus in C2, is stated. For the noncommutative classical group L1, the characteristic boundary of a kind of bounded symmetric domain in C4, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem on L1, if so, the solution is given explicitly.

INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.

A New Class of Complementarity Function and the Boundedness of Its Merit Function for Symmetric Cone Complementarity Problem

In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions(C-function). Moreover, its merit function has bounded level set under a weak condition.

Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems

One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.

基于Branch & Bound方法MIQP问题的求解及应用

研究基于 Branch & Bound (B&B) 方法的混合整数二次规划(Mixed Integer Quadratic Programming, MIQP)问题的求解,以及在一类混杂系统优化控制中的应用。B & B算法求解MIQP问题的过程,可视为对于一个二叉树的搜索。影响B & B算法寻优效率的两个主要方面是:分支变量的选择规则,以及树搜索策略。通过设定控制变量QPmax, 用以限制寻优过程求解QP问题的最大数目,可以在较短的时间内获得MIQP问题的满足整数约束条件次优解。利用MATLAB编制MIQP问题的求解程序,并在混杂系统优化控制中的应用,做了仿真计算。

A SUBSPACE PROJECTED CONJUGATE GRADIENT ALGORITHM FOR LARGE BOUND CONSTRAINED QUADRATIC PROGRAMMING

A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.

A New Homotopy Method for Nonlinear Complementarity Problems

In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method.

GLOBAL CONVERGENCE OF TRUST REGION ALGORITHM FOR EQUALITY AND BOUND CONSTRAINED NONLINEAR OPTIMIZATION

This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.

A New Type of Solution Method for the Generalized Linear Complementarity Problem over a Polyhedral Cone

This paper addresses the generalized linear complementarity problem （GLCP） over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over a closed polyhedral cone, and then propose a new type of method to solve the GLCP based on the error bound estimation. The global and R-linear convergence rate is established. The numerical experiments show the efficiency of the method.

Discrete differential evolution algorithm for integer linear bilevel programming problems

A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.

A SPARSE SUBSPACE TRUNCATED NEWTON METHOD FOR LARGE-SCALE BOUND CONSTRAINED NONLINEAR OPTIMIZATION

In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.

A SOLUTION OF A GENERAL EQUILIBRIUM PROBLEM

Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper.

Asymptotic Estimates for Second-Order Parameterized Singularly Perturbed Problem

The boundary value problem (BVP) for parameterized singularly perturbed second order nonlinear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented.

FEKETE AND SZEG INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER αON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN C^n

In this article, first, we establish the Fekete and Szego inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

A Priori Estimates of Solution of Parametrized Singularly Perturbed Problem

In this paper, we consider a parameterized singularly perturbed second order quasilinear boundary value problem. Asymptotic estimates for the solution and its first and second derivatives have been established. The theoretical estimates have been justified by concrete example.

Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition

We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig.

Computationally Efficient Problem Reformulations for Capacitated Lot Sizing Problem

In this article, we propose novel reformulations for capacitated lot sizing problem. These reformulations are the result of reducing the number of variables (by eliminating the backorder variable) or increasing the number of constraints (time capacity constraints) in the standard problem formulation. These reformulations are expected to reduce the computational time complexity of the problem. Their computational efficiency is evaluated later in this article through numerical analysis on randomly generated problems.