A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like i...

A quadratic inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be applied to the study of global existence of solutions to nonlinear PDE.

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

Abstract— A generalization of the L2-gain inequality based on nonlinear gains is considered. Using optimization and dynamic programming to characterize lower bounds for the minimal gain function for which this nonlinear L2-gain inequality holds, a technique for computation of nonlinear L2gain bounds is proposed. Some simple illustrative examples are explored.

This paper considers a general nonlinear econometric model framework that contains a large class of estimators defined as solutions to optimization problems. For this framework we derive several asymptotically equivalent forms of a test statistic for the local (in a way made precise in the paper) multivariate nonlinear inequality constraints test H: h(1) > 0 versus K: 1 E RK. We extend these re...

The Inequality-Growth Plateau We examine the (potentially nonlinear) relationship between inequality and growth using a method which does not require an a priori assumption on the underlying functional form. This approach reveals a plateau completely missed by commonly used (nonlinear) parametric approaches the economy first expands rapidly with a large decline in inequality, plateaus when ineq...

Recently, variational inequality theory has been extended and applied in various directions, see [6, 7, 8, 9, 10] and the references therein. In particular, Ding [1, 2, 3], and Ding and Tan [4] studied the existence of solutions for several nonlinear variational-like inequalities in reflexive Banach spaces. In this paper, a new class of general nonlinear variational-like inequalities in reflexi...

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...