A reformulation of the nonlinear complementarity problem (NCP) as an unconstrained minimization problem is considered. It is shown that any stationary point of the unconstrained objective function is already a solution of NCP if the mapping F involved in NCP is continuously differentiable and monotone. A descent algorithm is described which uses only function values of F. Some numerical results...

In a real Hilbert space, we aim to investigate two modified Mann subgradient-like methods find solution pseudo-monotone variational inequalities, which is also common fixed point of finite family nonexpansive mappings and an asymptotically mapping. We obtain strong convergence results for the sequences constructed by these proposed rules. give some examples illustrate our analysis.

In this paper, we introduce a modified Ishikawa-type proximal point algorithm for approximating common solution of minimization problem, monotone inclusion problem and fixed problem. We obtain strong convergence the proposed to finite family asymptotically demicontractive mapping in Hadamard spaces. Numerical example is given illustrate applicability our main result. Our results complement exte...

In this paper, we combine the subgradient extragradient method with the Halpern method for finding a solution of a variational inequality involving a monotone Lipschitz mapping in Banach spaces. By using the generalized projection operator and the Lyapunov functional introduced by Alber, we prove a strong convergence theorem. We also consider the problem of finding a common element of the set o...

Optimal control problems for possibly discontinuous entropy solutions of nonlinear multidimensional conservation laws with controls in source term and initial condition are considered. The control-to-state-mapping is analyzed by using monotone diierence schemes and existence results for optimal controls are proven. Moreover, a result on the convergence of optimal solutions of nite dimensional a...

In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and variational inclusion with two accretive operators. We obtain strong convergence theorem in setting Banach spaces. terms theorem, establish result (FPP) inequality (VIP) inverse-strongly monotone framework Hilbert Finally, is applied to deal...

Nonlinear Strip-Wise Affine Transformation George Moustris, Spyros .G. Tzafestas Intelligent Robotics and Automation Laboratory Department of Signals, Control and Robotics School of Electrical and Computer Engineering National Technical University of Athens Zographou 15773, Athens, Greece [email protected], [email protected] Abstract In this paper a piecewise linear homeomorphism ...

Solutions of a variational inequality problemdefined by a closed and convex set and a mapping are found by imposing conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to the composition of the projection onto the defining closed and convex set and the difference in the identity mapping and the defining mapping. One of these conditions is the iso...

the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...