Further Application of H

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) where f and g are H-differentiable. We describe H-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on the H-differentials of f and g, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g) to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for C1, semismooth, and locally Lipschitzian

Serum IL-21 level and its relation to activity and severity of alopecia areata

Background: Alopecia areata (AA) is a non-cicatricial alopecia that is postulated to be a hair-specific autoimmune disease, with genetic factors playing a role in disease susceptibility and severity. The disease presentation ranges from circular patches on the scalp to complete hair loss with devastating psychosocial consequences.Patients and methods: This was a case control study carried out on 40 patients diagnosed as alopecia areata. They were recruited from the outpatient clinic of Dermatology, Andrology and STDs Department, Mansoura University Hospitals. In addition 40 normal healthy subjects with matched age and sex were selected to act as a control group.Results: Serum levels of IL-21 were significantly increased in AA patients, and showed significant positive correlation with activity of the disease. Higher serum levels of IL-21 in active cases support its role as predictor of disease activity. There were no significant differences in IL-21 level with different SALT scores. Receiver Operating Characteristic (ROC) curve analysis of IL-21 was conducted to evaluate the sensitivity and specificity of serum IL-21 as a diagnostic index for AA. The AUC-ROC of IL-21 was excellent (0.962); and the best cut off point for IL-21 was determined to be 22.22 pg/ml. It was good predictive value. Its accuracy was 86.3%.Conclusions: The results of this study indicate that the serum IL-21 could be promising marker in the diagnosis of alopecia areata, and also can be used as prognostic marker of its activity

On Characterizations of Relatively P– and P0– Properties in Nonsmooth Functions

For H-differentiable function f from a closed rectangle Q in Rn into Rn, a result of Song, Gowda and Ravindran [On Characterizations of P- and P0-Properties in Nonsmooth Functions. Mathematics of Operations Research. 25: 400-408 (2000)] asserts that f is a P(P0)− function on Q if the HQ-differential TQ(x) at each x ∈ Q consisting of P(P0)− matrices. In this paper, we introduce the concepts of relatively P(P0)− properties in order to extend these results to nonsmooth functions when the underlying functions are H-differentiable.We give characterizations of relatively P(P0)− of vector nonsmooth functions. Also, our results give characterizations of relatively P(P0)− when the underlying functions are C1-functions, semismooth-functions, and for locally Lipschitzian functions. Moreover, we show useful applications of our results by giving illustrations to generalized complementarity problems

Solving Linear Bilevel Programming via Particle Swarm Algorithm with Heuristic Pattern Searc

A metaheuristic approach is proposed for solving linear bilevel programming problem using the Memetic Particle Swarm Algorithm which uses a Heuristic Pattern Search as the local search. The proposed algorithm has proven to be stable and capable of generating the optimal solution to the linear bilevel programming problem. The numerical results show that the metaheuristic approach is both feasible and efficient

Honey Bee Mating Optimization with Nelder-Mead for Constrained Optimization, Integer Programming and Minimax Problems

In this article, we propose a new hybrid Honey Bee Mating Optimization (HBMO) algorithm with simplex Nelder-Mead method in order to solve constrained optimization, integer programming and minimax problems. We call the proposed algorithm a hybrid Honey Bee Mating Optimization(HBMONM) algorithm. In the the proposed algorithm, we combine HBMO algorithm with Nelder-Mead method in order to refine the best obtained solution from the standard HBMO algorithm.We perform several experiments on a wide variety of well known test functions, 6 constrained optimization problems, 7 integer programming and 7 minimax benchmark problems.We compare the performance of HBMONMagainst standard HBMO algorithm and Genetic Algorithm (GA). In the majority of tests, HBMONM is shown to converge faster, and reach a better solution than both HBMO and GA in reasonable time