We obtain a characterization of the proximal normal cone to prox-regular subset Riemannian manifold and some properties Bouligand tangent cones these sets are presented. Moreover, we show that on an open neighborhood set, metric projection is locally Lipschitz it directionally differentiable at boundary points set. Finally, necessary condition for curve be minimizing in set derived.

After subtotal nephrectomy (STN), the remaining nephrons engage in hyperfiltration, which may be facilitated by a reduced sensitivity of the tubuloglomerular feedback (TGF) response to increased distal delivery. However, a muted TGF response would contradict the notion of remnant kidney as a prototype of angiotensin II (ANG II) excess, since ANG II normally sensitizes the TGF response and stimu...

The rediscovery of the affine scaling method in the late 80s was one of the turning points which led to a new chapter in Modern Optimization the Interior Point Methods (IPMs). The purpose of this paper is to show the intrinsic connections between Interior and Exterior Point methods (EPMs), which have been developed during the last 30 years. A class Ψ of smooth and strictly concave functions ψ :...

The minimization of an objective function over a constraint set can often be simplified if the “active manifold” of the constraints set can be correctly identified. In this work we present a simple subproblem, which can be used inside of any (convergent) optimization algorithm, that will identify the active manifold of a “prox-regular partly smooth” constraint set in a finite number of iterations.

A controlled sweeping process with prox-regular set, $$W^{1,2}$$ -controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions established local optimality conditions are derived via strong converging continuous approximations, whose state entirely resides the interior set. Consequently, subdifferentials smaller than standard ones now employed results.

Preferential oxidation of CO in the presence of excess hydrogen was studied on Pt/CeO2 with 5% metal loading. Catalytic data were similar to those observed on 1% Pt/CeO2 earlier [Wootsch et al. J. Catal. 225 (2004) 259]. The optimum temperature region is T≤373 K; conversion and selectivity of CO oxidation strongly decreased at higher temperatures. High-pressure XPS indicated CO adsorbed on plat...

The standard algorithms for solving large-scale convex–concave saddle point problems, or, more generally, variational inequalities with monotone operators, are proximal type algorithmswhich at every iteration need to compute a prox-mapping, that is, to minimize over problem’s domain X the sum of a linear form and the specific convex distance-generating function underlying the algorithms in ques...