For an inequality system defined by an infinite family of proper convex functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications. Under the new constraint qualifications, we provide necessary and/or sufficient conditions for the KKT rules to hold. Similarly, we provide characterizations for constrained minimization problems to have total Lagra...

Abstract Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation. This limiter happens to satisfy a stationary scalar hyperbolic inequality, within a constraint, for which we prove the existence and the uniqueness of the solution. Actually, this solution is shown to be the maximal elemen...

Existing interval constraint logic programming languages, such as BNR Prolog, work under the framework of interval narrowing and are deficient in solving systems of linear constraints over real numbers, which constitute an important class of problems in engineering and other applications. In this paper, we suggest to separate linear equality constraint solving from inequality and non-linear con...

In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed m...

5 This paper studies stability of error bounds for convex constraint systems 6 in Banach spaces. We show that certain known sufficient conditions for local 7 and global error bounds actually ensure error bounds for the family of func8 tions being in a sense small perturbations of the given one. A single inequality 9 as well as semi-infinite constraint systems are considered. 10 Mathematics Subj...

We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualifi...

Conjunctions of inequality predicates, or inequalities for short, have been utilized to represent conjunctive queries and semantic integrity constraints in semantic query processing systems (Klug 1988, Ullman 1989, Shenoy and Ozsoyoglu 1989, Guo et al. 1996). In conjunctive query containment problem, one needs to check whether a conjunction or set of inequality predicates implies an inequality....

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and “hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric met...

In our previous work, we developed TRAFFIC(X), a specification language for modeling bi-directional network flows featuring a type system with constrained polymorphism. In this paper, we present two ways to customize the constraint system: (1) when using linear inequality constraints for the constraint system, TRAFFIC(X) can describe flows with numeric properties such as MTU (maximum transmissi...