The recent development of non-monotone trust region methods

Abstract: Trust region methods are a class of numerical methods for optimization. They compute a trial step by solving a trust region sub-problem where a model function is minimized within a trust region. In this paper, we review recent results on non-monotone trust region methods for unconstrained optimization problems. Generally, non-monotone trust region algorithms with non-monotone technique are more effective than the traditional ones, especially when coping with some extreme nonlinear optimization problems. Results on trust region sub-problems and regularization methods are also discussed

Fixed Point of Strong Duality Pseudocontractive Mappings and Applications

Let E be a smooth Banach space with the dual , an operator is said to be α-strong duality pseudocontractive if , for all , where α is a nonnegative constant. An element is called a duality fixed point of T if . The purpose of this paper is to introduce the definition of α-strong duality pseudocontractive mappings and to study its fixed point problem and applications for operator equation and variational inequality problems

Combined effect of ultrasound-guided percutaneous abdominal paracentesis drainage and ulinastatin on severe acute pancreatitis

Purpose: To study the clinical effect of a combination of ultrasound-guided percutaneous abdominal paracentesis drainage (APD) and ulinastatin on severe acute pancreatitis (AP).Methods: A total of 94 patients with severe AP in Intensive Care Unit, Jiaozhou Central Hospital, Qingdao, from December 2017 to December 2018 were selected as the research subjects. They were divided into control and study groups, with 47 patients in each group. Patients in the control group underwent laparotomy drainage, while patients in the study group underwent ultrasound-guidedpercutaneous APD. Patients in both groups received ulinastatin perfusion. Subsequently, clinical effectsand other relevant indicators were determined.Results: Overall response was significantly higher in the study group than in the control group (p < 0.05). The times taken for disappearance of postoperative symptoms, normalization of serum amylase level, and hospitalization were significantly shorter in the study group than in the control group (p < 0.05). For every indicator, the study group exhibited more benefits after than before treatment; however, post-treatment levels of blood glucose, hemodiastase and urinary amylase were better than those in the control group (p < 0.05). Incidence of postoperative complications was lower in the study group than in control group (p < 0.05).Conclusion: The combination of ultrasound-guided percutaneous APD with ulinastatin produces marked beneficial effects on severe AP patients. It facilitates the remission of adverse symptoms, and enhances  normalization of indicator levels. Moreover, it displays low incidence of complications, better prognosis and recovery, and absence of post-operation infections

Minimum Thrust of a Morphing Unmanned Submersible Aerial Vehicle in the Water-to-Air Motion

This study proposes a new water-to-air motion pattern that combines morphing with power switch. Under the conditions of this pattern, the vehicle needs a certain thrust to avoid falling back after jumping out of the water. The minimum thrust is among the most important design parameters of a vehicle. The water-exit and take-off dynamic models of the vehicle are constructed through the force and motion analysis before and after morphing. The control model of the vehicle is created by analysing the control problem in the take-off motion. The minimum thrust at different initial water-exit angles is computed using the optimum searching algorithm. The following law is then established: the greater the initial water-exit angle, the smaller the minimum thrust required in the air. Such a relationship becomes insignificant when the initial water-exit angle exceeds 40°