We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the accelerated unconstrained optimization method -the Heavy Ball method. We explain non-standard behavior of the method discovered in practical applications. In addition, such non-monotonicity complicates the correct choice of the parameters in optimization methods. We propose to overcome this difficulty by introducing new Lyapunov function which should decrease monotonically. By use of this function convergence of the method is established under less restrictive assumptions (for instance, with the lack of convexity). We also suggest some restart techniques to speed up the method's convergence.

The analysis revealed factors that have an adverse effect on human health: artificial lighting (I =0.72); standing activity (I=0.63); monotonous movements (I =0.56); prolonged work at the computer (I =0.55). It was found that many pharmacy workers have chronic diseases: vascular pathology (29.4%), musculoskeletal pathology (28.4%), gastrointestinal tract pathology (27.5%); visual impairment (27.5%). It was found that 20.6% of pharmacy employees do not have breaks for rest and meal; 13.7% do not have the opportunity to take warm food at work; 35.3% have the biggest meal of the day in the evening. In the workplace, a set of factors that have an adverse effect on the health of pharmaceutical professionals has been identified; many workers have work-related chronic diseases; most pharmacists experience discomfort after work; some employers violate labour legislation by not providing specialists with breaks for rest and meal.