We consider the problem of finding target vectors for which the nonzero duality gap exists in the problem of convex optimization. An infinitesimal approach to the duality gap analysis of convex problems is proposed. The approach is based on finding the order of smallness and the proportionality coefficient of perturbation function of the original optimization problem. We show that in case of du...

The growth effects of schooling are often assumed to be exaggerated because of feedback effects from growth to schooling. This paper investigates the nexus between productivity growth and schooling at different levels using a sample of 19 OECD countries over the period 1870 to 2006. The empirical estimates show 1) that schooling is independent of expected growth and most other variables that ar...

Electrical coupling in circuits can produce non-intuitive circuit dynamics, as seen in both experimental work from the crustacean stomatogastric ganglion and in computational models inspired by the connectivity in this preparation. Ambiguities in interpreting the results of electrophysiological recordings can arise if sets of pre- or postsynaptic neurons are electrically coupled, or if the elec...

We present some Farkas-type results for inequality systems involving finitely many DC functions. To this end we use the so-called FenchelLagrange duality approach applied to an optimization problem with DC objective function and DC inequality constraints. Some recently obtained Farkas-type results are rediscovered as special cases of our main result.

Using a set-valued dual cost function we give a new approach to duality theory for linear vector optimization problems. We develop the theory very close to the scalar case. Especially, in contrast to known results, we avoid the appearance of a duality gap in case of b = 0. Examples are given.

Strong variants of the Operator Speed-up Theorem, Operator Gap Theorem and Compression Theorem are obtained using an effective version of Baire Category Theorem. It is also shown that all complexity classes of recursive predicates have effective measure zero in the space of recursive predicates and, on the other hand, the class of predicates with almost everywhere complexity above an arbitrary ...

A gauge function f(.) is a nonnegative convex function that is positively homogeneous and satisfies f(O)=O. Norms and pseudonorms are specific instances of a gauge function. This paper presents a gauge duality theory for a gauge program, which is the problem of minimizing the value of a gauge function f(.) over a convex set. The gauge dual program is also a gauge program, unlike the standard La...