In this paper, a new class of nonconvex sets and functions called strongly -convex sets and strongly -convex functions are introduced. This class is considered as a natural extension of strongly -convex sets and functions introduced in the literature. Some basic and differentiability properties related to strongly -convex functions are discussed. As an application to optimization problems, some optimality properties of constrained optimization problems are proved. In these optimization problems, either the objective function or the inequality constraints functions are strongly -convex.
Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope
... Show MoreBis-anthraquinones with a unique molecular backbone, (+)-2,2’-epicytoskyrin A (epi) and (+)-1,1′-bislunatin (bis), was produced by endophytic fungi Diaporthe sp GNBP-10 associated with Gambir plant (Uncaria gambier). Epi and bis possess robust antimicrobial activity toward various pathogens. This study focus on knowing the optimum condition of epi and bis production from Diaporthe sp GNBP-10. A series of culture media with various nutrient compositions was investigated in epi and bis production. The content of epi and bis was determined by measuring the area under the curve from TLC-densitometric (scanner) experiment. The linear regression analysis was then applied to obtain the results. The optimi
... Show MoreThe aim of the present study was to develop theophylline (TP) inhalable sustained delivery system by preparing solid lipid microparticles using glyceryl behenate (GB) and poloxamer 188 (PX) as a lipid carrier and a surfactant respectively. The method involves loading TP nanoparticles into the lipid using high shear homogenization – ultrasonication technique followed by lyophilization. The compositional variations and interactions were evaluated using response surface methodology, a Box – Behnken design of experiment (DOE). The DOE constructed using TP (X1), GB (X2) and PX (X3) levels as independent factors. Responses measured were the entrapment efficiency (% EE) (Y1), mass median
... Show MoreConstruction contractors usually undertake multiple construction projects simultaneously. Such a situation involves sharing different types of resources, including monetary, equipment, and manpower, which may become a major challenge in many cases. In this study, the financial aspects of working on multiple projects at a time are addressed and investigated. The study considers dealing with financial shortages by proposing a multi-project scheduling optimization model for profit maximization, while minimizing the total project duration. Optimization genetic algorithm and finance-based scheduling are used to produce feasible schedules that balance the finance of activities at any time w
Many objective optimizations (MaOO) algorithms that intends to solve problems with many objectives (MaOP) (i.e., the problem with more than three objectives) are widely used in various areas such as industrial manufacturing, transportation, sustainability, and even in the medical sector. Various approaches of MaOO algorithms are available and employed to handle different MaOP cases. In contrast, the performance of the MaOO algorithms assesses based on the balance between the convergence and diversity of the non-dominated solutions measured using different evaluation criteria of the quality performance indicators. Although many evaluation criteria are available, yet most of the evaluation and benchmarking of the MaOO with state-of-art a
... Show MoreIn this work, the photodetection performance of polyvinyl alcohol (PVA) nanofibers and its composite with yttrium oxide (Y2O3) at different concentrations (2.5, 5, 10) wt% are examined deposited on p-type Si with (111) orientation. Electrospinning technique was used to create nanofiber composites. Adding Y2O3 significantly impacts the PVA nanofibers where ultraviolet-visible (UV-Vis) spectroscopy optical absorption energy gap decreases with increased concentration (2.8, 2.6, and 2.3) eV. X-ray diffraction was used to investigate crystal structure, which is cubic structure. The chemical composition study was conducted using Fourier transform infrared spectroscopy (FTIR) spectra, which revealed the stretching vibrations related to the Y-O bon
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