We consider the simplest optimal control problem with one nonregular mixed constraint $G(x,u)\le0,$ i.e., such a that gradient $G_u(x, u)$ can vanish on surface $G = 0.$ Using Dubovitskii--Milyutin theorem approximate separation of convex cones, we prove first order necessary condition for weak minimum in form so-called local principle, which is formulated terms functions bounded variation, int...

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

Minimum (or minimal) principles are mathematical laws that were first used in physics: Hamilton's principle and Fermat's principle of least time are two famous example. In the past decade, a number of motor control theories have been proposed that are formally of the same kind as the minimum principles of physics, and some of these have been quite successful at predicting motor performance in a...

The principle of maximum information preservation has been successfully used to derive learning algorithms for self-organizing neural networks. In this paper, we state and apply the corresponding principle for supervised networks: the principle of minimum information loss. We do not propose a new learning algorithm, but rather a pruning algorithm which works to achieve minimum information loss ...

The main statistics used in rough set data analysis, the approximation quality, is of limited value when there is a choice of competing models for predicting a decision variable. In keeping within the rough set philosophy of non–invasive data analysis, we present three model selection criteria, using information theoretic entropy in the spirit of the minimum description length principle. Our ma...