During the past 15 years the topic of constraint databases (CDB) [2, 3] has evolved into a mature area of computer science with sound mathematical foundations and with a profound theoretical understanding of the expressive power of a variety of query languages. Constraint databases are especially suited for applications in which possibly infinite sets of continuous data, which have a geometric ...

Extended clauses are the basic formulas of the 0-1 constraint solver for the constraint logic programming language CLP(PB). We present a method for transforming an arbitrary linear 0-1 inequality into a set of extended clauses, such that the solution space remains invariant. After applying well-known linearization techniques on non-linear 0-1 constraints followed by the presented transformation...

In this paper, we introduce a constant positive linear dependence condition (CPLD), which is weaker than the Mangasarian–Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). We show that a limit point of a sequence of approximating Karush–Kuhn–Tucker (KKT) points is a KKT point if the CPLD holds there. We show that a KKT point satisfying the CPLD and ...

∗The work of the first and third authors was supported in part by the National Science Foundation under Grants DMI-9813057 and DMI-0422931, and by the US Department of Energy under Grant DEFG0204ER25655. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation or those ...

Datalog systems evaluate joins over arithmetic (in)equalities as a naive generate-and-test of Cartesian products. We exploit aggregates in a source-to-source transformation to reduce the size of Cartesian products and to improve performance. Our approach approximates the well-known propagation technique from Constraint Programming. Experimental evaluation shows good run time speed-ups on a rang...

Rank constraints on matrices emerge in many automatic control applications. In this short document we discuss how to rewrite the constraint into a polynomial equations of the elements in a the matrix. If addition semidefinite matrix constraints are included, the polynomial equations can be turned into an inequality. We also briefly discuss how to implement these polynomial constraints.

Rank constraints on matrices emerge in many automatic control applications. In this short document we discuss how to rewrite the constraint into a polynomial equations of the elements in a the matrix. If addition semidefinite matrix constraints are included, the polynomial equations can be turned into an inequality. We also briefly discuss how to implement these polynomial constraints.

By virtue of convexification techniques, we study best approximations to a closed set C in a Hilbert space as well as perturbation conditions relative to C and a nonlinear inequality system. Some results on equivalence of the best approximation and the basic constraint qualification are established.

We present a new version of first order necessary optimality conditions for a static minmax problem with inequality constraints in the parametric constraint case. These conditions, after some modification, turn out to characterize strict local minimizers of order one for the given problem.

B Abstract. The application and the performance of the neighboring optimal feedback scheme presented in Part 1 of this paper is demonstrated for the heating constrained cross-range maximization problem of a space-shuttle-orbiter-type vehicle. This problem contains ve state and two control variables and a state variable inequality constraint of order zero.