With the aid of some novel complementarity constraint quali cations, we derive some simpli ed primal-dual characterizations of a B-stationary point for a mathematical program with complementarity constraints (MPEC). The approach is based on a locally equivalent piecewise formulation of such a program near a feasible point. The simpli ed results, which rely heavily on a careful dissection and im...

A novel and interesting approach to infinite and infinitesimal numbers was recently proposed in a series of papers and a book by Y. Sergeyev. This novel numeral system is based on the use of a new infinite unit of measure (the number grossone, indicated by the numeral 1), the number of elements of the set, N, of natural numbers. Based on the use of 1, De Cosmis and De Leone [1] have then propos...

We derive firstand second-order necessary optimality conditions for set-constrained optimization problems under the constraint qualificationtype conditions significantly weaker than Robinson’s constraint qualification. Our development relies on the so-called 2-regularity concept, and unifies and extends the previous studies based on this concept. Specifically, in our setting constraints are giv...

Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, are a difficult class of constrained optimization problems. The feasible set has a very special structure and violates most of the standard constraint qualifications (CQs). Thus, the Karush-Kuhn-Tucker (KKT) conditions are not necessarily satisfied by minimizers and the convergence assumptions of many meth...

Investigation of optimality conditions has been one the most interesting topics in theory multiobjective optimisation problems (MOP). To derive necessary MOP, we consider assumptions called constraints qualifications. It is recognised that Guignard Constraint Qualification (GCQ) efficient and general assumption for scalar objective problems; however, GCQ does not ensure Karush-Kuhn Tucker (KKT)...

In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the mathematical program with complementarity constraints (MPCC) in replacing the set of nonnegative reals by second-order cones. There are difficulties in applying the classical Karush–Kuhn–Tucker (KKT) condition to the SOCMPCC directly since the usual constrai...

BACKGROUND Although there is consistent evidence that higher levels of education are associated with better health and reduced disease risk, there is little evidence on whether this is true throughout the lifecourse. This study examines whether additional higher educational qualifications acquired later on in adulthood are associated with a reduction in coronary heart disease (CHD) risk over an...

There is no parity of esteem between academic and vocational qualifications in the labour market. Data from the Labour Force Survey show that on average men and women working full-time with academic qualifications at one level in the national qualifications framework earn about the same as men and women with vocational qualifications set notionally one level higher. So those with A levels have ...

This paper deals with particular families of DC optimization problems involving suprema convex functions. We show that the specific structure this type function allows us to cover a variety in nonconvex programming. Necessary and sufficient optimality conditions for these are established, where some structural features conveniently exploited. More precisely, we derive necessary (global local) s...