Global optimization of a class of nonconvex quadratically constrained quadratic programming problems

In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.     

Existence of solutions for some non‐Fredholm integro‐differential equations with the bi‐Laplacian

We prove the existence of solutions for some semilinear elliptic equations in the appropriate H⁴ spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the previous results.     

一类具有边界摄动的非线性问题的渐近解及其可解性条件

利用摄动理论,讨论一类具有边界摄动的非线性问题.在适当的条件下,得出了这类问题的渐近解及其可解性条件,推广了一类近乎圆膜的振动问题所得的结果.     

Tractable classes of nonzero-sum open-loop Nash differential games: Theory and examples

This paper identifies some classes ofN-person nonzero-sum differential games that are tractable, in the sense that open-loop Nash strategies can be determined, either explicitly or qualitatively in terms of a phase-diagram portrait. The classes are characterized by conditions imposed on the Hamiltonians. Also, the underlying game structures needed to satisfy these conditions are characterized.The authors wish to thank V. Kaitala, Helsinki University of Technology, and the referees.     

Dominance solvability and cournot stability

In normal form games with single-valued best reply functions it is shown that dominance-solvability (resulting from successive elimination of dominated strategies) implies the global stability of the Cournot tatonnement process. When only two players are present, and the strategy spaces are one dimensional, these two notions actually coincide. A computational characterization of the two properties is given in a local sense as well as a sufficient condition for global dominance-solvability: an application to the Cournot-oligopoly model is proposed.     

Non-cooperative implementation: A survey of recent results

Strategic decentralization of collective decision-making is considered when the agents' behaviour is non-cooperative. Specifically they use dominant, maximin risk-avert or sophisticated strategies. The existing results applying these equilibrium concepts are reviewed in three familiar economically meaningful contexts: ordinal (as in voting), random (as in bargaining) and quasilinear (as in public goods problems).     

Qualitatively invertible matrices

Our purpose is to describe the properties of the class of n×n matrices such that some or all of the signs of the nonzero elements of the inverse matrix can be determined based only upon the knowledge of the signs of the matrix being inverted. Applications of such matrices can be found in the study of the testibility of economic theory, the stability of economic systems and the general ‘quality’ of solutions to large computer models.     

Kernel B-splines and interpolation

This paper applies difference operators to conditionally positive definite kernels in order to generate kernel -splines that have fast decay towards infinity. Interpolation by these new kernels provides better condition of the linear system, while the kernel -spline inherits the approximation orders from its native kernel. We proceed in two different ways: either the kernel -spline is constructed adaptively on the data knot set , or we use a fixed difference scheme and shift its associated kernel -spline around. In the latter case, the kernel -spline so obtained is strictly positive in general. Furthermore, special kernel -splines obtained by hexagonal second finite differences of multiquadrics are studied in more detail. We give suggestions in order to get a consistent improvement of the condition of the interpolation matrix in applications.     

一类Riemann-Hilbert边值逆问题

给出解析函数的一类R iem ann-H ilbert边值逆问题的数学提法,依据解析函数R iem ann-H ilbert边值问题的经典理论,讨论了此边值问题的可解性,给出了该边值问题的可解条件和解的表示式.