The derivation of multiplier-based optimality conditions for elliptic mathematical programs with equilibrium constraints (MPEC) is essential for the characterization of solutions and development of numerical methods. Though much can be said for broad classes of elliptic MPECs in both polyhedric and non-polyhedric settings, the calculation becomes significantly more complicated when additional c...

We study the largest number of sequences with the property that any two sequences do not contain specified pairs of patterns. We show that this number increases exponentially with the length of the sequences and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We illustrate a new heuristic for computing the joint spectral...

In calibrating the model, some of the parameter values are chosen based on data or recent empirical studies (summarized in Table 1 of the paper), and the remaining are obtained by finding the parameterization that best matches the steady state in the model to the average values in the American automobile industry over the 1994–2003 period. For the latter, we use the MPEC (Mathematical Programmi...

The hand with its pose and gesture is not easy to track with cameras. It is mostly because of a high number of degrees of freedom and a complex shape. Our algorithm is based on three dimensional clouds of points issued from stereovision in order to keep the depth information. The complex and organic aspect of the hand is modeled by an articulated skeleton on which metaballs are attached. We red...

[Puget, 2004] has shown that if the symmetry in a constraint satisfaction problem acts only on the variables and there is also an allDifferent constraint on the variables, the symmetry can be eliminated by adding a small number of constraints, linear in the number of variables. In this paper, Puget’s procedure for finding a set of symmetrybreaking constraints is extended to find all possible di...

Various models that incorporate concepts from Non-Cooperative Game Theory are described in the transport literature. Game Theory provides powerful tools for analysing transport systems, but these tools have some drawbacks that should be recognized. In the current paper we review games that describe transport problems and discuss them within a uniform context. Although the paper does not introdu...

We investigate the constraints on models of supermassive black hole (SMBH) and quasar formation obtainable from two recent observational developments: the discovery of luminous quasars at z ∼ 6, and estimates of the local mass density of SMBHs. If ∼ 90 per cent of this mass was accreted at redshifts z < ∼ 3, as suggested by the observed quasar luminosity functions, these joint constraints pose ...

We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are a...

We have proposed a method for dynamically posting symmetry breaking constraints to eliminate value interchangeability [1]. We now extend this method to work with any type of symmetry breaking constraint for any type of symmetry. We prove that this method is correct in general. That is, it only eliminates symmetric solutions. We also identify some simple conditions when it eliminates all symmetr...

Covering arrays have been studied for their applications to drug screening and software and hardware testing. In this paper, we model the problem as a constraint program. Our proposed models exploit non-binary (global) constraints, redundant modelling, channelling constraints, and symmetry breaking constraints. Our initial experiments show that with our best integrated model, we are able to eit...