Sensitivity analysis of extended general variational inequalities.
Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems
There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function converges...
Solution behaviour for parameter-dependent quasi-variational inequalities
Solution of projection problems over polytopes.
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...
Some characteristic quantities associated with homogeneous -type and -type functions.
Some combinatorial results about the operators with jumping nonlinearities
Some new existence, sensitivity and stability results for the nonlinear complementarity problem
In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence...
Systems of variational inequalities related to economic equilibrium
The duality theory for general convex quadratic programs
The nonlinear complementarity model of industrial symbiosis network equilibrium problem
In this paper, we propose an industrial symbiosis network equilibrium model by using nonlinear complementarity theory. The industrial symbiosis network consists of industrial producers, industrial consumers, industrial decomposers and demand markets, which imitates natural ecosystem by means of exchanging by-products and recycling useful materials exacted from wastes. The industrial producers and industrial consumers are assumed to be concerned with maximization of economic profits as well as minimization...
The shrinking projection method for solving variational inequality problems and fixed point problems in Banach spaces.
Two examples of the operators with jumping nonlinearities
Une procédure de purification pour les problèmes de complémentarité linéaire, monotones
Dans cet article, nous proposons une nouvelle méthode de purification pour les problèmes de complémentarité linéaire, monotones. Cette méthode associe à chaque itéré de la suite, générée par une méthode de points intérieurs, une base non nécessairement réalisable. Nous montrons que, sous les hypothèses de complémentarité stricte et de non dégénérescence, la suite des bases converge en un nombre fini d’itérations vers une base optimale qui donne une solution exacte du problème. Le procédé adopté...
Une procédure de purification pour les problèmes de complémentarité linéaire, monotones
Dans cet article, nous proposons une nouvelle méthode de purification pour les problèmes de complémentarité linéaire, monotones. Cette méthode associe à chaque itéré de la suite, générée par une méthode de points intérieurs, une base non nécessairement réalisable. Nous montrons que, sous les hypothèses de complémentarité stricte et de non dégénérescence, la suite des bases converge en un nombre fini d'itérations vers une base optimale qui donne une solution exacte du problème. Le procédé adopté...
Zur Dualitätstheorie bei linearen Optimierungsproblemen in halbgeordneten Vektorräumen.