Non-intersecting squared Bessel paths with one positive starting and ending point

We consider a model of n non-intersecting squared Bessel processes with one starting point a > 0 at time t = 0 and one ending point b > 0 at time t = T. After proper scaling, the paths fill out a region in the tx-plane. The region may come to the hard edge at 0 or may not, depending on the value of the product ab. We formulate a vector equilibrium problem for this model, which is defined for three measures, with upper constraints on the first and third measures and an external field on the second measure. It is shown that the limiting mean distribution of the paths at time t is given by the second component of the vector that minimizes this vector equilibrium problem. The proof is based on a steepest descent analysis for a 4 × 4 matrix-valued Riemann-Hilbert problem which characterizes the correlation kernel of the paths at time t. We also discuss the precise locations of the phase transitions.     

Topological pseudomonotonicity and vector equilibrium problems

In this paper, we introduce the topological pseudomonotonicity to vector valued bifunctions, and derive some existence results for vector equilibrium problems with the corresponding bifunctions topologically pseudomonotone. Some applications to vector variational inequalities and existence of Pareto optima are given.     

Singular perturbations of variational problems arising from a two-phase transition model

Given that, are two Lipschitz continuous functions of to ₊ and thatf(x, u, p) is a continuous function of × × ^N to [0, + [ such that, for everyx, f(x,·, 0) reaches its minimum value 0 at exactly two points(x) and(x), we prove the convergence ofF (u) = (1/) f (x, u, Du) dx when the perturbation parameter goes to zero. A formula is given for the limit functional and a general minimal interface criterium is deduced for a wide class of two-phase transition models. Earlier results of [19], [21], and [22] are extended with new proofs.     

Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems

We consider semidefinite monotone linear complementarity problems (SDLCP) in the space ⁿ of real symmetric n×n-matrices equipped with the cone ⁿ₊ of all symmetric positive semidefinite matrices. One may define weighted (using any Mⁿ₊₊ as weight) infeasible interior point paths by replacing the standard condition XY=rI, r>0, (that defines the usual central path) by (XY+YX)/2=rM. Under some mild assumptions (the most stringent is the existence of some strictly complementary solution of (SDLCP)), these paths have a limit as r0, and they depend analytically on all path parameters (such as r and M), even at the limit point r=0.Mathematics Subject Classification (1991): 90C33, 65K05     

Edgeworth equilibrium in a model of interregional economic relations

We introduce an analog of an Edgeworth equilibrium for a class of multiregional economic systems. We analyze the game-theoretic aspects of the coalition stability of regional development plans and establish a quite general existence theorem for an Edgeworth equilibrium. We discuss the questions of coincidence of the set of these equilibria with the fuzzy core and the set of theWalrasian equilibria of the multiregional systemin question.Our methods rest on a systematic accounting for the polyhedrality of the sets of balanced coalition plans.     

Scalarization and optimality conditions for vector equilibrium problems

In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems.     

Solution semicontinuity of parametric generalized vector equilibrium problems

In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.     

Sensitivity analysis of parametric weak vector equilibrium problems

In this paper, two implicit multifunction theorems are obtained. Then by using a set-valued gap function and the results obtained we study the sensitivity analysis of the solution mapping for a parametric weak vector equilibrium problem and obtain an explicit expression for the contingent derivative of the solution mapping.     

Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency

This paper deals with the relations between vector variational inequality problems and nonsmooth vector optimization problems using the concept of quasi efficiency. We identify the vector critical points, the weak quasi efficient points and the solutions of the weak vector variational inequality problems under generalized approximate convexity assumptions. To the best of our knowledge such results have not been established till now.     

Existence of solutions on weak vector equilibrium problems

Weak vector equilibrium problems with bi-variable mappings from product space of two bounded complete locally convex Hausdorff topological vector spaces to another topological vector space are studied. The existence theorems of solutions are proved by the FKKM fixed point theorem. Viscosity principle of vector equilibrium problems is dealt with. The relations between solutions of the vector equilibrium problem and those of its perturbation problem are presented.     

Efficient solutions and optimality conditions for vector equilibrium problems

Necessary optimality conditions for efficient solutions of unconstrained and vector equilibrium problems with equality and inequality constraints are derived. Under assumptions on generalized convexity, necessary optimality conditions for efficient solutions become sufficient optimality conditions. Note that it is not required here that the ordering cone in the objective space has a nonempty interior.     

Existence and stability of solutions for a class of generalized vector equilibrium problems

In this paper, two existence theorems concerning the strong efficient solutions and the weakly efficient solutions of generalized vector equilibrium problems are derived by using the Fan-KKM Theorem and an existence theorem for the efficient solutions of generalized vector equilibrium problems is established by using the scalarization method. Moreover, the lower semicontinuity of the strong efficient solution mapping and the weakly efficient solution mapping to parametric generalized vector equilibrium problems are showed under suitable conditions with neither monotonicity nor any information of the solution mappings. Finally, some applications to the vector optimization problems and the Stackelberg equilibrium problem are also given.     

Chebyshev scalarization of solutions to the vector equilibrium problems

In this paper, we give results on Chebyshev scalarization of weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution to the vector equilibrium problems without convexity assumptions.     

A characterization of super efficiency in vector equilibrium problems

In this paper, by using the Baire category theorem we give a characterization of superefficient solution for vector equilibrium problems in Banach space without the ordering cone having a bounded base.     

向量均衡问题的超有效性的对偶形式

在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念,并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解, C-超有效解, C-齐次超有效解,以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性,并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用,给出了向量优化问题各种超有效解的对偶形式.     

The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.     

Existence results for strong vector equilibrium problems and their applications

New existence results for the strong vector equilibrium problem are presented, relying on a well-known separation theorem in infinite-dimensional spaces. The main results are applied to strong cone saddle-points and strong vector variational inequalities providing new existence results, and furthermore they allow recovery of an earlier result from the literature.     

Generalization and sharpening of some duality relations for a class of vector optimization problems

We consider a class of vector optimization problems with linear restrictions in which each objective function is a sum of a linear function and of a norm of a linear vector function. Under some conditions we prove weak, direct and converse duality statements. In comparison with former papers the considered class is more general and our results are sharper.