Optimality conditions for nonsmooth mathematical programs with equilibrium constraints,using convexificators

In this paper, we deal with constraint qualifications, stationary concepts and optimality conditions for a nonsmooth mathematical program with equilibrium constraints (MPEC). The main tool in our study is the notion of convexificator. Using this notion, standard and MPEC Abadie and several other constraint qualifications are proposed and a comparison between them is presented. We also define nonsmooth stationary conditions based on the convexificators. In particular, we show that GS-stationary is the first-order optimality condition under generalized standard Abadie constraint qualification. Finally, sufficient conditions for global or local optimality are derived under some MPEC generalized convexity assumptions.     

界约束下算子方程最小二乘问题的条件梯度法

研究如下界约束下算子方程最小二乘问题:min x∈Ω‖L(X:A_1,…,At;B_1,…,B_t)-T‖~2,其中‖.‖为Frobenius范数,L(X:A_1…A_t;B_1,…,B_t)为关于X的线性矩阵算子(或齐次线性变换),Ai∈R~(p×m),B_j∈R~(n×q)i,j=1,…,n为算子L的系数矩阵,丁为右端矩阵,ΩR~(m×n)为界约束凸集合.提出了求解问题的条件梯度迭代算法及其简要收敛性分析,并给出条件梯度算法的几类加速形式.随机数据和图像恢复模型数据的实验结果表明说明算法是可行高效的.     

Multiplicity of solutions for Kirchhoff type equations involving critical Sobolev exponents in high dimension

In this paper, we study the following Kirchhoff‐type elliptic problem where is a bounded domain with smooth boundary ?Ω, a,b,λ,μ > 0 and 1 < q < 2^?=2N/(N ? 2). When N = 4, we obtain that there is a ground state solution to the problem for q∈(2,4) by using a variational methods constrained on the Nehari manifold and also show the problem possesses infinitely many negative energy solutions for q∈(1,2) by applying usual Krasnoselskii genus theory. In addition, we admit that there is a positive solution to the equations for N≥5 under some suitable conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal mean–variance investment and reinsurance problems for the risk model with common shock dependence

In this paper, we study the optimal investment–reinsurance problems in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of mean–variance, two cases are considered: One is the optimal mean–variance problem with bankruptcy prohibition, i.e., the wealth process of the insurer is not allowed to be below zero at any time, which is solved by standard martingale approach, and the closed form solutions are derived; The other is the optimal mean–variance problem without bankruptcy prohibition, which is discussed by a very different method—stochastic linear–quadratic control theory, and the explicit expressions of the optimal results are obtained either. In the end, a numerical example is given to illustrate the results and compare the values in the two cases.     

多层对称薄膜的光子晶体光波导设计

基于多层对称薄膜的反射镜作用,设计了一种工作波长位于1550nm附近的基于周期性多层膜的光子晶体光波导。由平板波导的相关理论分析了波长在1515~1587nm范围内电磁波在波导中的传输性质。研究表明TE模和TM模在波导都是基模传输,其功率约束因子(Γ)限制在0.99~1之间,说明波导近乎完全将光波限制在其中传输。在控光能力上这种结构要比普通的三层薄膜波导更具优势。利用周期性多层膜的光子带隙结构,可以构造具有超低损耗的全向带隙介质光波导。     

EFFECTS OF NONHOLONOMIC CONSTRAINT ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF LAGRANGIAN SYSTEMS

After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain.     

THE SOLUTION FOR THE GENERALIZED RICCATI ALGEBRAIC EQUATIONS OF LINEAR EQUALITY CONSTRAINT SYSTEM

I.IntroductionTheestablishmentofanalogytheorybetweencomputationalstructuralmechanicsalldoptimalcontrolisbasedonthesubstructuralchaintheoryinstructuralmechanicsandthelillearquadratic(LQ)controlprobleminoptimalcontrolllJ.Whendealillgwiththecontrolproblenlbyapplyingtheabovethe.ry,wecanrealizetheadvantagesofmethodsinstrLlcturalInechanicsl2'3].Howevermostworkhasbeenlimitedtothenon-constraintsystemandlittleworkhasbeendonefortheconstraintsystemsofLlr.InRef.I4],basedonthegeneralizedvariationalprin…     

具有主动约束层阻尼板的振动杂交控制*

本文研究了局部附加主动约束阻尼层(LACL)板的主、被动杂交控制问题.基于弹性、粘弹性、压电材料的本构关系,建立了系统的控制方程.利用Galerkin方法和GHM方法将偏微分方程转换为维数不高的常微分方程组,应用LQR方法进行了数值模拟.计算结果表明,这种主动和被动结合的杂交控制方式具有良好的控制效果.     

Regularity of Solution for Fully Nonlinear Second Order Elliptic Equation with Gradient Constraint

The existence and regularity of the solution for the fully nonlinear second order elliptic equation with gradient constraint are discussed in this paper. We prove the existence of the strong solution by choice of special penalty function, and obtain the local W^{2,∞} estimate of the solution by means of the theory of viscosity solution with the auxiliary function method.     

退化抛物型方程与单侧约束系统

本文讨论了一类非线性非自治多值的退化抛物型方程解的存在性和解的正则性等。它代表一类具非线性本构约束及不可微外约束的能量耗散的物理、力学和优化等问题。