Quasi-Equilibrium Problems and Constrained Multiobjective Games in Generalized Convex Space

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸａｎｄＹｂｅｎｏｎｅｍｐｔｙｓｅｔｓａｎｄ2 ＸｂｅｔｈｅｆａｍｉｌｙｏｆａｌｌｓｕｂｓｅｔｓｏｆＸ .ＬｅｔＴ :Ｘ→Ｙｂｅａｓｉｎｇｌｅ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,Ａ :Ｘ→ 2 Ｘｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,ψ :Ｘ×Ｙ×Ｘ→Ｒ∪ ±∞ ａｎｄｆ:Ｘ×Ｙ→Ｒ∪ ±∞ ｂｅｔｗｏｆｕｎｃｔｉｏｎｓ.Ｔｈｅｇｅｎｅｒａｌｑｕａｓｉ＿ｅｑｕｉｌｉｂｒｉｕｍｐｒｏｂｌｅｍＧＱＥＰ (Ｔ ,Ａ ,ψ)ｉｓｔｏｆｉｎｄ ^ｘ∈Ｘｓｕｃｈｔｈａｔ^ｘ∈Ａ( ^ｘ) ,ψ( ^ｘ ,Ｔ^ｘ ,ｙ)≤ 0…     

CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY CONVEX H-SPACES

IntroductionTheconceptofanequilibriumpointforann_persongamewasfirstintroducedbyNash[1,2 ],whoestablishedtheexistenceoftheequilibriumpointundercertainassumptions.Sincethen ,theNashequilibriumproblemforn_persongameshavebeenintensivelystudiedandextendedbyanumberofauthorsundervariousassumptionsanddifferentdirections.Theconstrainedgameswithfiniteorinfiniteplayersisanimportantgeneralizationofn_persongameswhichhavebeenwidelystudiedbymanyauthors.Recently ,muchattentionhasbeenfocusedonthegameproblemsw…     

Generalized constrained multiobjective games in locally <Emphasis Type="Italic">FC</Emphasis>-uniform spaces

A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.     

Constrained multiobjective games in locally convex<Emphasis Type="Italic">H</Emphasis>-spaces

A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied. By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem, several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces. These theorems improve, unify and generalize the corresponding results of the multiobjective games in recent literatures. Contributed by Ding Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Ding Xie-ping (1938-)     

PARETO EQUILIBRIA OF MULTICRITERIA GAMES WITHOUT COMPACTNESS，CONTINUITY AND CONCAVITY

ＰＡＲＥＴＯＥＱＵＩＬＩＢＲＩＡＯＦＭＵＬＴＩＣＲＩＴＥＲＩＡＧＡＭＥＳＷＩＴＨＯＵＴＣＯＭＰＡＣＴＮＥＳＳ,ＣＯＮＴＩＮＵＩＴＹＡＮＤＣＯＮＣＡＶＩＴＹＤｉｎｇＸｉｅｐｉｎｇ（丁协平）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ．ｂｙｕｓｉｎｇａｍｉｎ...     

On the Existence of Solutions for Stationary Mean-Field Games with Congestion

Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.     

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS IN LOCALLY G-CONVEX SPACES

IntroductionLetX ,YbetwotopologicalspacesandZbeanonemptyset.LetF∶X×X→ 2 Z,A∶X→ 2 XandC∶X→ 2 Zbeset_valuedmappingswhere2 ZdenotesthefamilyofallsubsetsofZ .　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅰ ) (inshort,GVQEP(Ⅰ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 1 )　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅱ ) (inshort,GVQEP(Ⅱ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 2 )　　…     

车辆主动悬架设计的约束H∞控制方法

针对线性离散时间系统,研究其时域硬约束下的H∞输出反馈控制问题。假定外界扰动能量有限,基于线性矩阵不等式处理方法,提出并证明了时域硬约束下H∞输出反馈控制器存在的充分条件,并应用于车辆主动悬架设计。四分之一车辆模型数值仿真结果表明,即使车辆模型参数存在不确定性,本文提出的控制器在提高车辆乘坐舒适性的同时,仍能很好地兼顾车辆的其他性能要求。     

A new equilibrium existence theorem of generalized game

ＡＮＥＷＥＱＵＩＬＩＢＲＩＵＭＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＯＦＧＥＮＥＲＡＬＩＺＥＤＧＡＭＥＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ）ＡＮＥＷＥＱＵＩＬＩＢＲＩＵＭＥＸＩＳＴＥＮＣＥＴＨＥ...     

General existence theorems for unilateral problems in continuum mechanics

The problem of minimizing a possibly non-convex and non-coercive functional is studied. Either necessary or sufficient conditions for the existence of solutions are given, involving a generalized recession functional, whose properties are discussed thoroughly. The abstract results are applied to find existence of equilibrium configurations of a deformable body subject to a system of applied forces and partially constrained to lie inside a possibly unbounded region.     

Noncompact infinite optimization and equilibria of constrained games in generalized convex spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＩｂｅａｎｙ (ｆｉｎｉｔｅｏｒｉｎｆｉｎｉｔｅ)ｉｎｄｅｘｓｅｔａｎｄｆｏｒｅａｃｈｉ∈Ｉ,Ｘｉｂｅａｔｏｐｏｌｏｇｉｃａｌｓｐａｃｅ.ＷｅｕｓｅｔｈｅｎｏｔａｔｉｏｎＸ =∏ｉ∈ＩＸｉ　ａｎｄ　Ｘｉ=∏ｊ∈Ｉ,ｊ≠ｉＸｊ.Ｆｏｒｅａｃｈｘ∈Ｘ ,ｘｉｄｅｎｏｔｅｓｉｔｓｉｔｈｃｏｏｒｄｉｎａｔｅａｎｄｘｉｔｈｅｐｒｏｊｅｃｔｉｏｎｏｆｘｏｎＸｉ.Ｗｒｉｔｅｘ=(ｘｉ,ｘｉ) .Ｆｏｒｅａｃｈｉ∈Ｉ,ｌｅｔＦｉ:Ｘｉ → 2 Ｘｉｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇａｎｄｆｉ:Ｘ →Ｒ …     

LINEAR QUADRATIC NONZERO-SUM DIFFERENTIAL GAMES WITH RANDOM JUMPS

IntroductionFully coupled forward-backward stochastic differential equations with Brownian motioncan be encountered in the optimization problem when we apply stochastic maximum principleand in mathematics finance when we consider large investor in securit…     

LINEAR QUADRATIC NONZERO-SUM DIFFERENTIAL GAMES WITH RANDOM JUMP

The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.     

On the active part of the stress for elastic materials with internal constraints

Constitutive equations for constrained elastic materials prescribe a whole set of possible stresses for each deformation. We prove the existence of a normalization procedure for determining the active part of the stress through a single-valued response function which is both frame-indifferent and invariant under the same symmetry group of the given constitutive equation.     

Stability of Schrödinger-Poisson type equations

Variational methods are used to study the nonlinear SchrSdinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Hamiltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.     

Sub/superharmonic oscillations and the perturbation procedure

The problem of sub/super and harmonic oscillations of non-linear systems is considered in this paper. This is made possible by the development of a modified version of the constrained Linstedt-Poincare perturbation procedure. The generality of the procedure is such that the existence of sub/super and harmonic oscillations can be simultaneously handled. Furthermore, the methodology developed is such that no a priori knowledge of solution form is necessary to establish the existence of such oscillation modes. Based on the approach, the steady response of Duffing's equation wherein sub/super and harmonic oscillations exist is studied in detail.     

Stability of Schr(o)dinger-Poisson type equations

Variational methods are used to study the nonlinear Schr(o)dinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Halniltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.     

Similar normal mode vibrations in certain conservative systems with two degrees-of-freedom

The existence of similar normal mode vibrations for the problem of two masses constrained to move on arbitrary smooth coplanar curves and coupled one to the other by a spring is considered. Three curve shapes which admit similar normal modes are found. In addition, the quadratures expressing the relation between frequency and amplitude for two cases are integrated in terms of known functions for the special case of a linear spring.     

Internal constraints in linear elasticity

Sufficient conditions are obtained for continuous dependence of solutions of boundary value problems of linear elasticity on internal constraints. Arbitrary hyperelastic materials with arbitrary (linear) internal constraints are included. In particular the results of Bramble and Payne, Kobelkov, Mikhlin for homogeneous, isotropic, incompressible materials are obtained as a special case. In the case of boundary value problem of place, a compatibility condition is obtained between the internal constraints and the boundary data which is necessary for the existence of solutions. With a further coercivity assumption on the compliance tensor, it is shown that the compatibility condition is also sufficient for existence. An orthogonal decomposition theorem for second order tensor fields modeled after Weyl's decomposition of solenoidal and gradient fields leads to the variational formulation of the problem and existence theorems.Almost all the results here apply to materials both with or without internal constraints. For internally constrained materials however, the verification of certain hypothesis is surprisingly non-trivial as indicated by the computation in the appendix.     

Perturbation of symmetries of Birkhoff system and adiabatic invariants

The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then these results are generalized to the constrained Birkhoff system. One example is presented to illustrate these results. The project supported by the National Natural Science Foundation (19972010) and the Doctoral Program Foundation of Institution of Higher Education of China and the Natural Science Foundation of Henan Province