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Mathematical program with vertical complementarity constraints (MPVCC) plays an important role in economics and engineering. Due to the vertical complementarity structure, most of the standard constraint qualifications fail to hold at a feasible point. Without constraint qualifications, the Karush–Kuhn–Tucker (KKT) conditions are not necessary optimality conditions. The classical methods for solving constrained optimization problems applied to MPVCC are likely to fail. It is necessary to establish efficient algorithms for solving MPVCC from both theoretical and numerical points of view. We present an algorithm to obtain stationarity of MPVCC by solving a sequence of Scholtes regularized problems. We consider the Scholtes regularization method with the sequence of approximate KKT points only. We prove that, under strictly weaker constraint qualifications, the accumulation point of the approximate KKT points is Clarke (C-) stationary point. In particular, we can get Mordukhovich (M-) or strongly (S-) stationary point under additional assumptions. From these results, we apply an augmented Lagrangian method to obtain a solution of MPVCC and give the convergence analysis. In particular, the accumulation point of the generated iterates is an S-stationary point if some boundedness conditions hold. The numerical results show that it is an effective way to solve MPVCC. [ABSTRACT FROM AUTHOR]

The paper considers a class of vector optimization problems with cone constrained generalized equations. By virtue of advanced tools of variational analysis and generalized differentiation, a limiting normal cone of the graph of the normal cone constrained by the second-order cone is obtained. Based on the calmness condition, we derive an upper estimate of the coderivative for a composite set-valued mapping. The necessary optimality condition for the problem is established under the linear independent constraint qualification. As a special case, the obtained optimality condition is simplified with the help of strict complementarity relaxation conditions. The numerical results on different examples are given to illustrate the efficiency of the optimality conditions. [ABSTRACT FROM AUTHOR]

This paper mainly establishes the sensitivity analysis of a multiobjective optimization problem with parameterized quasi-variational inequalities (QVIs). Using the (regular) coderivative of the associated epigraphical multifunction, the (regular) subdifferentials of the efficient frontier maps are estimated, which involve the (regular) coderivatives of the solution mapping to the parameterized QVIs. Under the linear independent constraint qualification, the defined auxiliary set-valued mappings in the parameterized QVIs are clam. The detailed formulae of subdifferentials of the efficient frontier maps are obtained and examples are simultaneously provided for analyzing and illustrating the obtained results. [ABSTRACT FROM AUTHOR]

Chuanxiong Rhizoma is a traditional Chinese medicinal material mainly produced in Sichuan and Chongqing of China. In recent years, the cadmium content in Chuanxiong Rhizoma produced in most of the genuine producing areas has exceeded the standard, which makes Chuanxiong Rhizoma difficult to be exported. To solve the problem of excessive cadmium content in soil, this study employed the MaxEnt model to simulate the potential geographic distribution of Ligusticum chuanxiong and evaluate important environmental factors, and re-plan its ecologically suitable areas based on the mineral distribution characteristics and soil cadmium pollution status. The results showed that the places suitable for L. chuanxiong growing covered an area of 335 523.69 km~2, mainly in central and eastern Sichuan, southern Shaanxi and most parts of Chongqing. Among them, the highly suitable areas of L. chuanxiong were mainly concentrated in Chengdu, Ya'an, Deyang, and Mianyang. Solar radiation, annual precipitation, and annual range of temperature were evaluated as important variables affecting the distribution of L. chuanxiong, with the contribution rates of 62.3%, 13.3%, and 6.8%, respectively. In addition, Qionglai county, Chongqing county, Mianyang city(Youxian district and Fucheng district), Qingchuan county, and Xinjin county were classified into the first-class ecologically suitable zone, covering a total area of 2 768.87 km~2. The se-cond-class ecologically suitable zone was even wider, involving such counties as Tongjiang county, Renshou county, Jianyang county, and Nanjiang county, and the total area reached 43 616.92 km~2. The re-planning of the ecologically suitable areas for L. chuanxiong has provided strong data support for the cultivation and resource development of L. chuanxiong and also new ideas for solving the problem of excessive cadmium content in L. chuanxiong.

Resources survey of traditional Chinese medicine and reserves estimation are found to be the most important issues for the protection and utilization of traditional Chinese medicine resources, this paper used multi-spatial resolution remote sensing images (RS) , geographic information systems (GIS) and global positioning system (GPS) , to establish Scutellaria resources survey of 3S data platform. Combined with the traditional field survey methods, small-scale habitat types were established based on different skullcap reserve estimation model, which can estimate reserves of the wild Scutellaria in Beijing-Tianjin-Hebei region and improve the estimation accuracy. It can provide an important parameter for the fourth national survey of traditional Chinese medicine resources and traditional Chinese medicine reserves estimates based on 3S technology by multiple spatial scales model.

Background/aims: The optimal timing for laparoscopic cholecystectomy (LC) in acute cholecystitis (AC) remains controversial. In this study, we aggressively performed three types of LC techniques in AC patients at different time with our care procedure., Methodology: Forty-three patients with AC were retrospectively divided into two groups: Group one (n=16, within 72 hrs at the onset of symptoms) and Group two (n=27, beyond 72 hrs after the onset of symptoms). Standard, subtotal or prograde cholecystectomy were performed for all cases, depending on the fragility of gallbladder wall, difficulty of gallbladder dissection, assurance of Calot's triangle and quality of retraction over Hartman pouch., Results: There were no statistical differences between both groups with regards to age, operation time, length of hospital stay and complications. Gangrenous cholecystitis was found in 6.3% of cases in Group one and 26.9% in Group two, although not statistically different. Four cases (two in each of groups) underwent prograde cholecystectomy and four cases in the group 2 received subtotal cholecystectomy; all with longer operation time and length of stay, as compared to standard cholecystectomy. None of the 43 patients was converted to open procedure. Complications in this study were minor., Conclusions: LC can be safely performed in patients with AC with special care, regardless of the duration between the onset of symptoms and operation. In addition to standard procedures, subtotal and prograde cholecystectomy could help to manage inflammatory gallbladder and obscured Calot's triangle.

Objective: To observe the different effects between Mahuang (Herba Ephedra Sinicae) and Wuweizi (Fructus Schisandrae Chinensis) on the pathological changes of rats with bleomycin A(5)-induced pulmonary fibrosis., Methods: Ninety Wistar rats were randomly divided into sham operation group, model group, hydrocortisone group, Herba Ephedra Sinicae group, Fructus Schisandrae Chinensis group and Herba Ephedra Sinicae plus Fructus Schisandrae Chinensis group. There were 16 rats in each group except the sham operation group (10 rats). Pulmonary fibrosis was induced by a single intratracheal injection of bleomycin A5. Hematoxylin and eosin straining and immunohistochemical method were used after 7- and 28-day treatment to observe the pathology of lung injury, measure the inner diameter of pulmonary arterioles and the density of nuclear membrane., Results: Compared with the sham operation group at 7 and 28 d, alveolar inflammation level was significantly increased in the model group (P<0.01). Alveolar inflammation level was decreased obviously in the hydrocortisone group (P<0.05) after 7- and 28-day treatment as compared with the model group, and that in Herba Ephedra Sinicae plus Fructus Schisandrae Chinensis group was also decreased obviously (P<0.05) at 28 d. Compared with the sham operation group, nuclear density of the model group was increased, while its inner diameter was decreased (P<0.05). In the Fructus Schisandrae Chinensis group, Herba Ephedra Sinicae plus Fructus Schisandrae Chinensis group and hydrocortisone group, the nuclear density was decreased (P<0.05) as compared with the model group. Inner diameter in the Herba Ephedra Sinicae group, Herba Ephedra Sinicae plus Fructus Schisandrae Chinensis group and hydrocortisone group was higher than that in the model group (P<0.05). Microvessel density of the model group was obviously higher than that of the sham operation group (P<0.05). Compared with the model group, Herba Ephedra Sinicae plus Fructus Schisandrae Chinensis group and hydrocortisone group had lower microvessel density (P<0.05)., Conclusion: Herba Ephedra Sinicae combined with Fructus Schisandrae Chinensis can restrain pulmonary artery injury. The nuclear density and microvessel density can be reduced by Fructus Schisandrae Chinensis, while Herba Ephedra Sinicae can increase the inner diameter.

Objective: To optimize the molding formula of refined Xiong-gui sustained release pills, types and assorted dosages of water-soluble and non water-soluble drug carrier were studied., Method: An orthogonal design was performed to sift the pill formulation. The processing conditions were determining in terms of roundness, hardness, viscosity, fluidity, easily drop., Result and Conclusion: According to the final optimal formula, the amount of drug release can be detected instantly, while remaining over 80% at 10 h.