‎in this paper, using the idea of convexificators, we study boundedness and nonemptiness of lagrange multipliers satisfying the first order necessary conditions. we consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. within this context, define generalized mangasarian-fromovitz constraint qualification and show t...

We study a procurement setting in which the buyer seeks a low price but will not allocate the contract to a supplier who has not passed qualification screening. Qualification screening is costly for the buyer, involving product tests, site visits, and interviews. In addition to a qualified incumbent supplier, the buyer has an entrant of unknown qualification. The buyer wishes to run a price-onl...

In this paper we describe the model-based approach to tool qualification starting from the process model for the determination of the qualification need until the model for test and qualification. The model-based approach can automate many steps from checking the syntactical requirements completeness until the determination whether all requirements have been implemented and successfully tested....

We study the predictability of emergent phenomena in complex systems. Using nearest-neighbor, one-dimensional cellular automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounti...

In this paper we study the qualification problem in theories of reasoning about actions and change and the link of this problem to properties of representation for expressing such theories. We examine the interaction of the qualification problem with the frame and ramification problems and show how an integrated solution to these problems can be developed where the frame persistence and constra...

In the past, students in England and Wales born within the first five months of the academic year could leave school one term earlier than those born later in the year. Focusing on women, those who were required to stay on an extra term more frequently hold some academic qualification. Using having been required to stay on as an exogenous factor affecting academic attainment, we find that holdi...

The emergence of complex new ground states at interfaces has been identified as one of the most promising routes to highly tunable nanoscale materials. Despite recent progress, isolating and controlling the underlying mechanisms behind these emergent properties remains among the most challenging materials physics problems to date. In particular, generating ferromagnetism localized at the interf...

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 ...

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification from Minchenko and Stakhovski that was called RCR. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and asserts t...