Relaxation in nonconvex optimal control problems described by fractional differential equations

We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously.     

Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions

We derive a Weierstrass-type formula for conformal Lagrangian immersions in Euclidean 4-space, and show that the data satisfies an equation similar to Dirac equation with complex potential. Alternatively this representation has a simple formulation using quaternions. We apply it to the Hamiltonian stationary case and construct all possible tori, thus obtaining a first approach to a moduli space in terms of a simple algebraic-geometric problem on the plane. We also classify Hamiltonian stationary Klein bottles and show they self-intersect. Received: January 25, 2000.     

Optimal Control Problems with State Constraint Governed by Magnetohydrodynamic Equations

This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by MHD equations with state constraint of pointwise type in three-dimension. Strong results in two-dimension also are given.     

超Li系统的Bargmann对称约束和双非线性化

给出超Li系统的一个显式对称约束和关于其Lax对的双非线性化.在此对称约束下,超Li系统的时间部分和空间部分分别被约化为有限维Liouville可积超Li系统.     

A branch-and-cut algorithm for the Multiple Steiner TSP with Order constraints

The paper deals with a problem motivated by survivability issues in multilayer IP-over-WDM telecommunication networks. Given a set of traffic demands for which we know a survivable routing in the IP layer, our purpose is to look for the corresponding survivable topology in the WDM layer. The problem amounts to Multiple Steiner TSPs with order constraints. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We also present new valid inequalities and discuss their facial aspect. Based on this, we devise a Branch-and-cut algorithm and present preliminary computational results.     

On solution sequences of the singular Liouville equations with an integral constraint

In this paper,we analyze the blow-up behavior of sequences{uk}satisfying the following conditionsΔuk=|x|2αk V k eukinΩ,(0.1)whereΩR2,V k→V in C1,|Vk|≤A,0a≤Vk≤b,0≤αk→α∈(0,∞),andΩ|x|2αkeuk dx≤Λ1.(0.2)Furthermore,we assume that there exists someq∈(1,2)such that rq 2Br(p)|uk|qdx≤Λ2(0.3)for anyB r(p)Ω.As a result,we give a new proof of the concentration-compactness theorem for the mean feld equation.     

带有控制-状态混合约束的时滞Volterra型积分系统的最优控制问题

对带有控制-状态混合约束的一类受控时滞Volterra型积分系统,导出了其最优控制的一组必要条件和一组充分条件．     

一类多维0-1背包问题的约束归并方法

提出一种新的关于多维背包(Multi-dimensions Knapsack Problem,MKP)的约束替代问题,MKP是NP-完全问题,称这种约束替代方法为不等式单约束平面生成法.叙述了单约束不等平面生成算法的基本思想,证明了此方法的一些性质及化简问题后所得到的新问题MKPS与原问题MKP的等价性.最后用实例证实了这种化简方法及其有效性。     

Non-Noether Conserved Quantity of Nonholonomic System Having Variable Mass and Unilateral Constraints

Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The differential equations of motion of the system are given. The determining equations of Lie symmetrical transformations of the system under infinitesimal transformations are constructed. The Hojman‘s conservation theorem of the system is established. Finally, we give an example to illustrate the application of the result.