Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization assumes convexity or strong convexity of each function. In this paper, we extend this problem into the non-convex setting using variance reduction techniques, ...

A Lavrentiev prox-regularization method for optimal control problems with pointwise state constraints is introduced where both the objective function and the constraints are regularized. The convergence of the controls generated by the iterative Lavrentiev prox-regularization algorithm is studied. For a sequence of regularization parameters that converges to zero, strong convergence of the gene...

AIMS To evaluate the relative merits of proxymetacaine-fluorescein (PROX-FLU) and lignocaine-fluorescein (LIG-FLU) when used to perform applanation tonometry. METHODS This prospective, masked, double blind study assessed several aspects of the tonometry process-the duration of the stinging sensation and degree of discomfort, the extent of reflex lacrimation induced, the need for subsequent te...

The CO content of hydrogen feed to proton exchange membrane fuel cells (PEMFC) must be kept under 1-100 ppm for their proper operation. This can be achieved by using catalysts able to selectively oxidize CO in the presence of excess hydrogen (PROX). The present study reports on the mechanism of PROX reaction on Pt/CeO2 catalyst, by using catalytic tests, in-situ DRIFTS, high-pressure XPS, HRTEM...

— In this paper, we deal with sweeping processes on (possibly infinitedimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the framework of such manifolds. Especially we introduce the concept of local prox-regularity of a closed subset in accordance with the geometrical features of th...

Factors determining lymphatic differentiation in the adult organism are not yet well characterized. We have made the observation that mixed primary cultures of dermal blood endothelial cells (BEC) and lymphatic endothelial cells (LEC) grown under standard conditions change expression of markers during subculture: After passage 6, they uniformly express LEC-specific markers Prox-1 and podoplanin...

The objective of this research consisted of developing the two following thermal food processing software: “F-CALC” is software developed to carry out thermal process calculations based on the wellknown Ball's formula method, and “OPT-PROx” is software for thermal food processing optimization based on variable retort temperature processing and global optimization technique. Time-temperature dat...

Abstract In the setting of $\operatorname{CAT}(\kappa)$ CAT(?) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under assumption linear metric...

Preferential CO oxidation (PROX) was investigated by using dealloyed nanoporous gold (NPG) catalyst under ambient conditions. Systematic investigations were carried out to characterize its catalytic performance by varying reaction parameters such as temperature and co-existence of CO2 and H2O, which revealed that NPG was a highly active and selective catalyst for PROX, especially at low tempera...