化不等式约束问题为无约束的广义可微限域精确罚函数方法

本文给出了广义可微精确罚函数的概念及一类所谓广义限域可微精确罚函数.本文预先选定罚因子,将不等式约束问题化为单一的无约束问题,并给出了具全局收敛性的算法.本文的罚函数构造简单,假设条件少而且算法的构造与收敛性结果是独特的.     

正定矩阵的樊■不等式

本文对正定矩阵建立了樊■不等式,从而证明Wang C. L.的猜测(见《数学研究与评论》,1989年第4期)为真.     

A variational inequality approach for the determination of oligopolistic market equilibrium

This paper presents an alternative approach to that by Murphy, Sherali and Soyster [13] for computing market equilibria with mathematical programming methods. This approach is based upon a variational inequality representation of the problem and the use of a diagonalization/relaxation algorithm.     

A new algorithm for solving variational inequalities with application to the traffic assignment problem

The variational inequality problem in Euclidian space is formulated as a nonconvex, nondifferentiable optimization problem. We show that any stationary point is optimal, and we propose a solution algorithm that decreases the nondifferential objective monotonically. Application to the asymmetric traffic assignment problem is considered.Research supported by C.R.S.H. (Canada) grant #410-81-0722-RL and F.C.A.C. (Québec) grant # 83-AS-0026.     

Pinchings and Norms of Scaled Triangular Matrices

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that $$\|D^{-1}UD\|\ge\|U\|$$ for any matrix norm that is reduced by a pinching. In addition to known examples -weakly unitarily invariant norms - we show that any matrix norm defined by $$\| A \|^{\underline{\underline {{\rm def}}} } \mathop {\max }\limits_{x \ne 0,y \ne 0} {{{\mathop{\rm Re}\nolimits} (x^*Ay)} \over {\phi (x)\psi (y)}},$$ where θ (.) and y (.) are two absolute vector norms, has this property. This includes l p operator norms as a special case.     

On variational inequality approach to nash dynamic game of oil stockpiling ∗

Oil market disruption and strategic stockpiling are consideredin this work. A variational inequality approach is developed.The model treated here is more general than previous work.It is established that the Nash equilibrium is characterized by a system of inequalities. A sufficient condition for the existence and uniqueness of the Nash equilibrium is derived and an efficient iterative algorithm is proposed and analyzed     

Inequality problems with Nonlocally Lipschitz Energy Functional: Existence Results and Applications to Nonsmooth Mechanics

We give an existence result for a double eigenvalue problem in Hemivariational Inequalities whose energetic functional is not locally Lipschitz. It is used a finite dimensional approach based on Kakutani's fixed point theorem.     

Inequality averse multi-utilitarian bargaining solutions

This paper introduces and analyzes the class of inequality averse multi-utilitarian solutions for cooperative bargaining problems. We show that generalized Gini solutions and inequality averse Choquet solutions are particular cases of this new multi-valued solution concept and provide a complete characterization in which an invariance property, consisting of a weakening of both the linear invariance axiom in Blackorby et al. (Econometrica 62:1161–1178, 1994) and the restricted invariance axiom in Ok and Zhou (Games Econ Behav 33:249–264, 2000), plays an important role. Moreover, by relaxing the assumptions involved in the characterization, the class is extended to include inequality loving multi-utilitarian solutions which are also studied in the paper.     

A type of efficient feasible SQP algorithms for inequality constrained optimization

In this paper, motivated by Zhu et al. methods [Z.B. Zhu, K.C. Zhang, J.B. Jian, An improved SQP algorithm for inequality constrained optimization, Math. Meth. Oper. Res. 58 (2003) 271-282; Zhibin Zhu, Jinbao Jian, An efficient feasible SQP algorithm for inequality constrained optimization, Nonlinear Anal. Real World Appl. 10(2) (2009) 1220-1228], we propose a type of efficient feasible SQP algorithms to solve nonlinear inequality constrained optimization problems. By solving only one QP subproblem with a subset of the constraints estimated as active, a class of revised feasible descent directions are generated per single iteration. These methods are implementable and globally convergent. We also prove that the algorithms have superlinear convergence rate under some mild conditions.     

Some Theorems on Meromorphic Univalent Functions

In this paper, we will show some deviation theorems and theorems of rotational angles in classes of Σ(p) and Σ(p,q) of meromorphic univalent functions.