In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construc...In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.展开更多
A L463^5 Box-Behnken design was used for developing a model to predict and optimize the molecular weight （Mw ） of polypropylene （PP） ; a second-order polynomial regression equation was derived to predict responses...A L463^5 Box-Behnken design was used for developing a model to predict and optimize the molecular weight （Mw ） of polypropylene （PP） ; a second-order polynomial regression equation was derived to predict responses. The significance of variables and their interactions were tested by means of the ANOVA with 95% confidence limits; the standardized effects were investigated by Pareto chart, the optimum values of the selected variables were obtained by analyzing the response surface contour plots. The optimized Mw value of 1. 217 × 10^5 g/mol was very close to the industrial value （ （ 1.22 ±0. 004） ×10^6 g/tool） at the optimum values.展开更多
基金Supported by the National Natural Science Foundation of China(No.11101420,11331012,71271204)
文摘In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.
基金Supported by the R&D Program of Catalyst Company,SINOPEC(G8101-11-ZS-0016*)
文摘A L463^5 Box-Behnken design was used for developing a model to predict and optimize the molecular weight （Mw ） of polypropylene （PP） ; a second-order polynomial regression equation was derived to predict responses. The significance of variables and their interactions were tested by means of the ANOVA with 95% confidence limits; the standardized effects were investigated by Pareto chart, the optimum values of the selected variables were obtained by analyzing the response surface contour plots. The optimized Mw value of 1. 217 × 10^5 g/mol was very close to the industrial value （ （ 1.22 ±0. 004） ×10^6 g/tool） at the optimum values.
