In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investiga...In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investigate the relationship between two variables. The novel approach involves collecting elementary “y” data and subsequently analyzing the asymptotic cumulative or demulative (opposite of cumulative) Y data. In part I, we examine the connection between the common linear numbers and ideal nonlinear numbers. In part II, we delve into the relationship between X-ray energy and the radiation transmission for various thin film materials. The fundamental physical law asserts that the nonlinear change in continuous variable Y is negatively proportional to the nonlinear change in continuous variable X, expressed mathematically as dα = −Kdβ. Here: dα {Y, Yu, Yb} represents the change in Y, with Yu and Yb denoting the upper and baseline asymptote of Y. dβ {X, Xu, Xb} represents the change in X, with Xu and Xb denoting the upper and baseline asymptote of X. K represents the proportionality constant or rate constant, which varies based on equation arrangement. K is the key inferential factor for describing physical phenomena.展开更多
We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the...We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the constraints are partitioned into several parts,and the entry of our filter consists of these different parts.Not only the criteria for accepting a trial step would be relaxed,but the individual behavior of each part of constraints is considered.One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears.The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used.We prove that our algorithm is globally convergent to KKT points under the constant positive generators(CPG)condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification(MFCQ)and the constant positive linear dependence(CPLD).Numerical results are presented to show the efficiency of the algorithm.展开更多
文摘In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investigate the relationship between two variables. The novel approach involves collecting elementary “y” data and subsequently analyzing the asymptotic cumulative or demulative (opposite of cumulative) Y data. In part I, we examine the connection between the common linear numbers and ideal nonlinear numbers. In part II, we delve into the relationship between X-ray energy and the radiation transmission for various thin film materials. The fundamental physical law asserts that the nonlinear change in continuous variable Y is negatively proportional to the nonlinear change in continuous variable X, expressed mathematically as dα = −Kdβ. Here: dα {Y, Yu, Yb} represents the change in Y, with Yu and Yb denoting the upper and baseline asymptote of Y. dβ {X, Xu, Xb} represents the change in X, with Xu and Xb denoting the upper and baseline asymptote of X. K represents the proportionality constant or rate constant, which varies based on equation arrangement. K is the key inferential factor for describing physical phenomena.
基金This work is supported by National Science Founda-tion of China(No.11601318)Equipment Manufacturing Systems and Optimization(No.13XKJC01).
文摘We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the constraints are partitioned into several parts,and the entry of our filter consists of these different parts.Not only the criteria for accepting a trial step would be relaxed,but the individual behavior of each part of constraints is considered.One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears.The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used.We prove that our algorithm is globally convergent to KKT points under the constant positive generators(CPG)condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification(MFCQ)and the constant positive linear dependence(CPLD).Numerical results are presented to show the efficiency of the algorithm.
