We discuss several fundamental questions concerning the problem of minimizing a nonlinear function subject to a set of inequality constraints. We begin by asking: What makes the problem intrinsically diicult to solve, and which characterizations of the solution make its solution more tractable? This leads to a discussion of two important methods of solution: active set and interior points. We m...

Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to L-minimum norm control problems, L∞norm minimization, and a class of ...

Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The approach reduces the solution of the equation to that of an optimization problem in the idempotent algebra setting. Based on the approach, existence and uniquen...

We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the layer variable φ, endowed with periodic boundary conditions. We analyze the long-time behavior of the solutions within the theory of infinite-dimensional dissipative dynamical systems. We first prove...

regulations of use of social networks, as one of the key components in these networks, serve an important role in controlling the flow of traffic. the study of the harmonization of these terms and regulations can be a significant step to avoid congestion and (users’) rejection in the network. harmonization of traffic control regulations (tcr) among social networks is one of the best solutions...

The use of IT equipment has become a part of every day. However, each device that is part of cyberspace should be secured against unauthorized use. It is very important to know the basics of these security devices, but also the basics of safe conduct their owners. This information should be part of every curriculum computer science education in primary and secondary schools. Therefore, the work...

A logarithmic fourth-order parabolic equation in one space dimension with periodic boundary conditions is analyzed. Using a new semidiscrete approximation in time, a first-order entropy–entropy dissipation inequality is proved. Passing to the limit of vanishing time discretization parameter, some regularity results are deduced. Moreover, it is shown that the solution is strictly positive for la...

The generalized bilevel programming problem (GBLP) is a bilevel mathematical program where the lower level is a variational inequality. In this paper we prove that if the objective function of a GBLP is uniformly Lipschitz continuous in the lower level decision variable with respect to the upper level decision variable, then using certain uniform parametric error bounds as penalty functions giv...

For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverse-convex inequalities which are consequence of the constrained syst...

199 © 2012 Guilford Publications, Inc. The authors thank the members of the University of Virginia Implicit Social Cognition Lab for their helpful comments. This research was supported by Project Implicit and Ghent University Grant BOF/ GOA2006/001. Correspondence concerning this article should be sent to Colin Tucker Smith, Ghent University, Henri Dunantlaan 2, 9000 Ghent, Belgium. E-mail: col...